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zb%RBhk^m2klv!C84+@>@P(6DRu`AJZ-cFu?;cHuE4Sy^uZ|ML2N5_0cpH3p>gPp*HHXVheWXAEKl Date: Thu, 24 Oct 2024 22:05:36 -0500 Subject: [PATCH 3/6] Updated the nelson ODE function, (made it nicer to look at) and added parameters --- markdown/AstroChem/nelson.md | 300 +++++++++++++++++++---------------- 1 file changed, 161 insertions(+), 139 deletions(-) diff --git a/markdown/AstroChem/nelson.md b/markdown/AstroChem/nelson.md index b18f242ed..6397eddae 100644 --- a/markdown/AstroChem/nelson.md +++ b/markdown/AstroChem/nelson.md @@ -1,5 +1,5 @@ --- -author: "Stella Offner and Chris Rackauckas" +author: "Nina De La Torre (Advised by Stella Offner) and Chris Rackauckas" title: "Nelson Work-Precision Diagrams" --- ```julia @@ -11,151 +11,173 @@ using ODEInterface, ODEInterfaceDiffEq ```julia -T = 10 -Av = 2 # This is what depotic uses for visual extinction -Go = 1.7 # I think despotic uses 1.7 -n_H = 611 -shield = 1 - -function Nelson_ODE(du,u,p,t) - # 1: H2 - #= du[1] = -1.2e-17 * u[1] + - n_H * (1.9e-6 * u[2] * u[3]) / (T^0.54) - - n_H * 4e-16 * u[1] * u[12] - - n_H * 7e-15 * u[1] * u[5] + - n_H * 1.7e-9 * u[10] * u[2] + - n_H * 2e-9 * u[2] * u[6] + - n_H * 2e-9 * u[2] * u[14] + - n_H * 8e-10 * u[2] * u[8] =# - du[1] = 0 - - # 2: H3+ - du[2] = 1.2e-17 * u[1] + - n_H * (-1.9e-6 * u[3] * u[2]) / (T^0.54) - - n_H * 1.7e-9 * u[10] * u[2] - - n_H * 2e-9 * u[2] * u[6] - - n_H * 2e-9 * u[2] * u[14] - - n_H * 8e-10 * u[2] * u[8] - - # 3: e - du[3] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - - n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - - n_H * (3.3e-5 * u[11] * u[3]) / T + - 1.2e-17 * u[1] - - n_H * (1.9e-6 * u[3] * u[2]) / (T^0.54) + - 6.8e-18 * u[4] - - n_H * (9e-11 * u[3] * u[5]) / (T^0.64) + - 3e-10 * Go * exp(-3 * Av) * u[6] + - n_H * 2e-9 * u[2] * u[13] ## CHECK I added this extra term from a CR ionization reaction - + 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction - - - # 4: He - du[4] = n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - - 6.8e-18 * u[4] + - n_H * 7e-15 * u[1] * u[5] + - n_H * 1.6e-9 * u[10] * u[5] - #du[4] = 0 - - # 5: He+ 6.8e-18 or 1.1 - du[5] = 6.8e-18 * u[4] - - n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - - n_H * 7e-15 * u[1] * u[5] - - n_H * 1.6e-9 * u[10] * u[5] - #u[5] = 0 - - # 6: C - du[6] = n_H * (1.4e-10 * u[3] * u[12]) / (T^0.61) - - n_H * 2e-9 * u[2] * u[6] - - n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] + - 1e-9 * Go * exp(-1.5 * Av) * u[7] - - 3e-10 * Go * exp(-3 * Av) * u[6] + - 1e-10 * Go * exp(-3 * Av) * u[10] * shield - - # 7: CHx - du[7] = n_H * (-2e-10) * u[7] * u[8] + - n_H * 4e-16 * u[1] * u[12] + - n_H * 2e-9 * u[2] * u[6] - - 1e-9 * Go * u[7] * exp(-1.5 * Av) - - # 8: O - du[8] = n_H * (-2e-10) * u[7] * u[8] + - n_H * 1.6e-9 * u[10] * u[5] - - n_H * 8e-10 * u[2] * u[8] + - 5e-10 * Go * exp(-1.7 * Av) * u[9] + - 1e-10 * Go * exp(-3 * Av) * u[10] * shield - - # 9: OHx - du[9] = n_H * (-1e-9) * u[9] * u[12] + - n_H * 8e-10 * u[2] * u[8] - - n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - - 5e-10 * Go * exp(-1.7 * Av) * u[9] - - # 10: CO - du[10] = n_H * (3.3e-5 * u[11] * u[3]) / T + - n_H * 2e-10 * u[7] * u[8] - - n_H * 1.7e-9 * u[10] * u[2] - - n_H * 1.6e-9 * u[10] * u[5] + - n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - - 1e-10 * Go * exp(-3 * Av) * u[10] + - 1.5e-10 * Go * exp(-2.5 * Av) * u[11] * shield - - # 11: HCO+ - du[11] = n_H * (-3.3e-5 * u[11] * u[3]) / T + - n_H * 1e-9 * u[9] * u[12] + - n_H * 1.7e-9 * u[10] * u[2] - - 1.5e-10 * Go * exp(-2.5 * Av) * u[11] - - # 12: C+ - du[12] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - - n_H * 4e-16 * u[1] * u[12] - - n_H * 1e-9 * u[9] * u[12] + - n_H * 1.6e-9 * u[10] * u[5] + - 3e-10 * Go * exp(-3 * Av) * u[6] - - # 13: M+ - du[13] = n_H * (-3.8e-10 * u[13] * u[3]) / (T^0.65) + - n_H * 2e-9 * u[2] * u[14] - + 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction - - # 14: M - du[14] = n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - - n_H * 2e-9 * u[2] * u[14] - - 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction +#= +The ODE function defined below models the reduced carbon-oxygen +chemistry network of Nelson & Langer (1999, ApJ, 524, 923). + +This Julia ODE function was written by Nina De La Torre advised by Dr. Stella Offner. +The solution was compared with results derived by DESPOTIC, (Mark Krumholz, 2013) +a code to Derive the Energetics and Spectra of Optically Thick Insterstellar Clouds. +DESPOTIC has pre-defined networks, one of them coming from the Nelson & Langer paper, +so the initial conditions and parameters were meant to mimic those from DESPOTIC. + + Parameter definitions: + T = 10 --> Tempurature (Kelvin) + Av = 2 --> V-Band Extinction + G₀ = 1.7 --> Go; "a factor that determines the flux of FUV radiation relative to the standard interstellar value (G₀ = 1) as reported by Habing (1968)." + n_H = 611 --> Hydrogen Number Density + shield = 1 --> "CO self-shielding factor of van Dishoeck & Black (1988), taken from Bergin et al. (1995)" +=# + +function Nelson!(du,u,p,t) + T, Av, Go, n_H, shield = p + + # 1: H2 + du[1] = -1.2e-17 * u[1] + + n_H * (1.9e-6 * u[2] * u[3]) / (T^0.54) - + n_H * 4e-16 * u[1] * u[12] - + n_H * 7e-15 * u[1] * u[5] + + n_H * 1.7e-9 * u[10] * u[2] + + n_H * 2e-9 * u[2] * u[6] + + n_H * 2e-9 * u[2] * u[14] + + n_H * 8e-10 * u[2] * u[8] + + # 2: H3+ + du[2] = 1.2e-17 * u[1] + + n_H * (-1.9e-6 * u[3] * u[2]) / (T^0.54) - + n_H * 1.7e-9 * u[10] * u[2] - + n_H * 2e-9 * u[2] * u[6] - + n_H * 2e-9 * u[2] * u[14] - + n_H * 8e-10 * u[2] * u[8] + + # 3: e + du[3] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - + n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - + n_H * (3.3e-5 * u[11] * u[3]) / T + + 1.2e-17 * u[1] - + n_H * (1.9e-6 * u[3] * u[2]) / (T^0.54) + + 6.8e-18 * u[4] - + n_H * (9e-11 * u[3] * u[5]) / (T^0.64) + + 3e-10 * Go * exp(-3 * Av) * u[6] + + n_H * 2e-9 * u[2] * u[13] + + 2.0e-10 * Go * exp(-1.9 * Av) * u[14] + + # 4: He + du[4] = n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - + 6.8e-18 * u[4] + + n_H * 7e-15 * u[1] * u[5] + + n_H * 1.6e-9 * u[10] * u[5] + + # 5: He+ + du[5] = 6.8e-18 * u[4] - + n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - + n_H * 7e-15 * u[1] * u[5] - + n_H * 1.6e-9 * u[10] * u[5] + + # 6: C + du[6] = n_H * (1.4e-10 * u[3] * u[12]) / (T^0.61) - + n_H * 2e-9 * u[2] * u[6] - + n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] + + 1e-9 * Go * exp(-1.5 * Av) * u[7] - + 3e-10 * Go * exp(-3 * Av) * u[6] + + 1e-10 * Go * exp(-3 * Av) * u[10] * shield + + # 7: CHx + du[7] = n_H * (-2e-10) * u[7] * u[8] + + n_H * 4e-16 * u[1] * u[12] + + n_H * 2e-9 * u[2] * u[6] - + 1e-9 * Go * u[7] * exp(-1.5 * Av) + + # 8: O + du[8] = n_H * (-2e-10) * u[7] * u[8] + + n_H * 1.6e-9 * u[10] * u[5] - + n_H * 8e-10 * u[2] * u[8] + + 5e-10 * Go * exp(-1.7 * Av) * u[9] + + 1e-10 * Go * exp(-3 * Av) * u[10] * shield + + # 9: OHx + du[9] = n_H * (-1e-9) * u[9] * u[12] + + n_H * 8e-10 * u[2] * u[8] - + n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - + 5e-10 * Go * exp(-1.7 * Av) * u[9] + + # 10: CO + du[10] = n_H * (3.3e-5 * u[11] * u[3]) / T + + n_H * 2e-10 * u[7] * u[8] - + n_H * 1.7e-9 * u[10] * u[2] - + n_H * 1.6e-9 * u[10] * u[5] + + n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - + 1e-10 * Go * exp(-3 * Av) * u[10] + + 1.5e-10 * Go * exp(-2.5 * Av) * u[11] * shield + + # 11: HCO+ + du[11] = n_H * (-3.3e-5 * u[11] * u[3]) / T + + n_H * 1e-9 * u[9] * u[12] + + n_H * 1.7e-9 * u[10] * u[2] - + 1.5e-10 * Go * exp(-2.5 * Av) * u[11] + + # 12: C+ + du[12] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - + n_H * 4e-16 * u[1] * u[12] - + n_H * 1e-9 * u[9] * u[12] + + n_H * 1.6e-9 * u[10] * u[5] + + 3e-10 * Go * exp(-3 * Av) * u[6] + + # 13: M+ + du[13] = n_H * (-3.8e-10 * u[13] * u[3]) / (T^0.65) + + n_H * 2e-9 * u[2] * u[14] + + 2.0e-10 * Go * exp(-1.9 * Av) * u[14] + + # 14: M + du[14] = n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - + n_H * 2e-9 * u[2] * u[14] - + 2.0e-10 * Go * exp(-1.9 * Av) * u[14] end - -u0 = [0.5 ; # 1: H2 yep? - 9.059e-9 ; # 2: H3+ yep - 2.0e-4 ; # 3: e yep - 0.1 ; # 4: He SEE lines 535 NL99 - 7.866e-7 ; # 5: He+ yep? should be 2.622e-5 - 0.0 ; # 6: C yep - 0.0 ; # 7: CHx yep - 0.0004 ; # 8: O yep - 0.0 ; # 9: OHx yep - 0.0 ; # 10: CO yep - 0.0 ; # 11: HCO+ yep - 0.0002 ; # 12: C+ yep - 2.0e-7 ; # 13: M+ yep - 2.0e-7 ] # 14: M yep - - -tspan = (0.0, 30 * 3.16e10) # ~30 thousand yrs - -prob = ODEProblem(Nelson_ODE, u0, tspan) +# Set the Timespan, Parameters, and Initial Conditions +seconds_per_year = 3600 * 24 * 365 +tspan = (0.0, 30000 * seconds_per_year) # ~30 thousand yrs + +params = (10, # T + 2, # Av + 1.7, # Go + 611, # n_H + 1) # shield + +u0 = [0.5, # 1: H2 + 9.059e-9, # 2: H3+ + 2.0e-4, # 3: e + 0.1, # 4: He + 7.866e-7, # 5: He+ + 0.0, # 6: C + 0.0, # 7: CHx + 0.0004, # 8: O + 0.0, # 9: OHx + 0.0, # 10: CO + 0.0, # 11: HCO+ + 0.0002, # 12: C+ + 2.0e-7, # 13: M+ + 2.0e-7] # 14: M + + +prob = ODEProblem(Nelson!, u0, tspan, params) refsol = solve(prob, Vern9(), abstol=1e-14, reltol=1e-14) +sol2 = solve(prob, FBDF()) +sol3 = solve(prob, QNDF()) +sol4 = solve(prob, CVODE_BDF()) -using Plots -plot(sol; yscale=:log10, idxs = (0,5)) -``` +using Plots +colors = palette(:acton, 5) +p1 = plot(refsol, vars = (0,11), lc=colors[1], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ Reference solution") +p2 = plot(sol2, vars = (0,11), lc=colors[2], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using FBDF") +p3 = plot(sol3, vars = (0,11), lc=colors[3], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using QNDF") +p4 = plot(sol4, vars = (0,11), lc=colors[4], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using CVODE FBDF") +combined_plot = plot(p1, p2, p3, p4, layout=(4, 1), dpi = 600, pallete=:acton) +display(combined_plot) ``` -Error: UndefVarError: `sol` not defined -``` - - +![](figures/nelson_compare.png) From 16f73a6bd91880c7f8b04f2d1cc506478f2eaa23 Mon Sep 17 00:00:00 2001 From: Ninadlt <166744945+nnd389@users.noreply.github.com> Date: Thu, 24 Oct 2024 22:07:06 -0500 Subject: [PATCH 4/6] Updated the nelson ODE function, (made it nicer to look at) and added parameters --- script/AstroChem/nelson.jl | 292 ++++++++++++++++++++----------------- 1 file changed, 159 insertions(+), 133 deletions(-) diff --git a/script/AstroChem/nelson.jl b/script/AstroChem/nelson.jl index 38a14dc8a..324ece1fc 100644 --- a/script/AstroChem/nelson.jl +++ b/script/AstroChem/nelson.jl @@ -5,150 +5,176 @@ using Sundials, LSODA using ODEInterface, ODEInterfaceDiffEq -T = 10 -Av = 2 # This is what depotic uses for visual extinction -Go = 1.7 # I think despotic uses 1.7 -n_H = 611 -shield = 1 - -function Nelson_ODE(du,u,p,t) - # 1: H2 - #= du[1] = -1.2e-17 * u[1] + - n_H * (1.9e-6 * u[2] * u[3]) / (T^0.54) - - n_H * 4e-16 * u[1] * u[12] - - n_H * 7e-15 * u[1] * u[5] + - n_H * 1.7e-9 * u[10] * u[2] + - n_H * 2e-9 * u[2] * u[6] + - n_H * 2e-9 * u[2] * u[14] + - n_H * 8e-10 * u[2] * u[8] =# - du[1] = 0 - - # 2: H3+ - du[2] = 1.2e-17 * u[1] + - n_H * (-1.9e-6 * u[3] * u[2]) / (T^0.54) - - n_H * 1.7e-9 * u[10] * u[2] - - n_H * 2e-9 * u[2] * u[6] - - n_H * 2e-9 * u[2] * u[14] - - n_H * 8e-10 * u[2] * u[8] - - # 3: e - du[3] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - - n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - - n_H * (3.3e-5 * u[11] * u[3]) / T + - 1.2e-17 * u[1] - - n_H * (1.9e-6 * u[3] * u[2]) / (T^0.54) + - 6.8e-18 * u[4] - - n_H * (9e-11 * u[3] * u[5]) / (T^0.64) + - 3e-10 * Go * exp(-3 * Av) * u[6] + - n_H * 2e-9 * u[2] * u[13] ## CHECK I added this extra term from a CR ionization reaction - + 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction - - - # 4: He - du[4] = n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - - 6.8e-18 * u[4] + - n_H * 7e-15 * u[1] * u[5] + - n_H * 1.6e-9 * u[10] * u[5] - #du[4] = 0 - - # 5: He+ 6.8e-18 or 1.1 - du[5] = 6.8e-18 * u[4] - - n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - - n_H * 7e-15 * u[1] * u[5] - - n_H * 1.6e-9 * u[10] * u[5] - #u[5] = 0 - - # 6: C - du[6] = n_H * (1.4e-10 * u[3] * u[12]) / (T^0.61) - - n_H * 2e-9 * u[2] * u[6] - - n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] + - 1e-9 * Go * exp(-1.5 * Av) * u[7] - - 3e-10 * Go * exp(-3 * Av) * u[6] + - 1e-10 * Go * exp(-3 * Av) * u[10] * shield - - # 7: CHx - du[7] = n_H * (-2e-10) * u[7] * u[8] + - n_H * 4e-16 * u[1] * u[12] + - n_H * 2e-9 * u[2] * u[6] - - 1e-9 * Go * u[7] * exp(-1.5 * Av) - - # 8: O - du[8] = n_H * (-2e-10) * u[7] * u[8] + - n_H * 1.6e-9 * u[10] * u[5] - - n_H * 8e-10 * u[2] * u[8] + - 5e-10 * Go * exp(-1.7 * Av) * u[9] + - 1e-10 * Go * exp(-3 * Av) * u[10] * shield - - # 9: OHx - du[9] = n_H * (-1e-9) * u[9] * u[12] + - n_H * 8e-10 * u[2] * u[8] - - n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - - 5e-10 * Go * exp(-1.7 * Av) * u[9] - - # 10: CO - du[10] = n_H * (3.3e-5 * u[11] * u[3]) / T + - n_H * 2e-10 * u[7] * u[8] - - n_H * 1.7e-9 * u[10] * u[2] - - n_H * 1.6e-9 * u[10] * u[5] + - n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - - 1e-10 * Go * exp(-3 * Av) * u[10] + - 1.5e-10 * Go * exp(-2.5 * Av) * u[11] * shield - - # 11: HCO+ - du[11] = n_H * (-3.3e-5 * u[11] * u[3]) / T + - n_H * 1e-9 * u[9] * u[12] + - n_H * 1.7e-9 * u[10] * u[2] - - 1.5e-10 * Go * exp(-2.5 * Av) * u[11] - - # 12: C+ - du[12] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - - n_H * 4e-16 * u[1] * u[12] - - n_H * 1e-9 * u[9] * u[12] + - n_H * 1.6e-9 * u[10] * u[5] + - 3e-10 * Go * exp(-3 * Av) * u[6] - - # 13: M+ - du[13] = n_H * (-3.8e-10 * u[13] * u[3]) / (T^0.65) + - n_H * 2e-9 * u[2] * u[14] - + 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction - - # 14: M - du[14] = n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - - n_H * 2e-9 * u[2] * u[14] - - 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction +#= +The ODE function defined below models the reduced carbon-oxygen +chemistry network of Nelson & Langer (1999, ApJ, 524, 923). + +This Julia ODE function was written by Nina De La Torre advised by Dr. Stella Offner. +The solution was compared with results derived by DESPOTIC, (Mark Krumholz, 2013) +a code to Derive the Energetics and Spectra of Optically Thick Insterstellar Clouds. +DESPOTIC has pre-defined networks, one of them coming from the Nelson & Langer paper, +so the initial conditions and parameters were meant to mimic those from DESPOTIC. + + Parameter definitions: + T = 10 --> Tempurature (Kelvin) + Av = 2 --> V-Band Extinction + G₀ = 1.7 --> Go; "a factor that determines the flux of FUV radiation relative to the standard interstellar value (G₀ = 1) as reported by Habing (1968)." + n_H = 611 --> Hydrogen Number Density + shield = 1 --> "CO self-shielding factor of van Dishoeck & Black (1988), taken from Bergin et al. (1995)" +=# + +function Nelson!(du,u,p,t) + T, Av, Go, n_H, shield = p + + # 1: H2 + du[1] = -1.2e-17 * u[1] + + n_H * (1.9e-6 * u[2] * u[3]) / (T^0.54) - + n_H * 4e-16 * u[1] * u[12] - + n_H * 7e-15 * u[1] * u[5] + + n_H * 1.7e-9 * u[10] * u[2] + + n_H * 2e-9 * u[2] * u[6] + + n_H * 2e-9 * u[2] * u[14] + + n_H * 8e-10 * u[2] * u[8] + + # 2: H3+ + du[2] = 1.2e-17 * u[1] + + n_H * (-1.9e-6 * u[3] * u[2]) / (T^0.54) - + n_H * 1.7e-9 * u[10] * u[2] - + n_H * 2e-9 * u[2] * u[6] - + n_H * 2e-9 * u[2] * u[14] - + n_H * 8e-10 * u[2] * u[8] + + # 3: e + du[3] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - + n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - + n_H * (3.3e-5 * u[11] * u[3]) / T + + 1.2e-17 * u[1] - + n_H * (1.9e-6 * u[3] * u[2]) / (T^0.54) + + 6.8e-18 * u[4] - + n_H * (9e-11 * u[3] * u[5]) / (T^0.64) + + 3e-10 * Go * exp(-3 * Av) * u[6] + + n_H * 2e-9 * u[2] * u[13] + + 2.0e-10 * Go * exp(-1.9 * Av) * u[14] + + # 4: He + du[4] = n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - + 6.8e-18 * u[4] + + n_H * 7e-15 * u[1] * u[5] + + n_H * 1.6e-9 * u[10] * u[5] + + # 5: He+ + du[5] = 6.8e-18 * u[4] - + n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - + n_H * 7e-15 * u[1] * u[5] - + n_H * 1.6e-9 * u[10] * u[5] + + # 6: C + du[6] = n_H * (1.4e-10 * u[3] * u[12]) / (T^0.61) - + n_H * 2e-9 * u[2] * u[6] - + n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] + + 1e-9 * Go * exp(-1.5 * Av) * u[7] - + 3e-10 * Go * exp(-3 * Av) * u[6] + + 1e-10 * Go * exp(-3 * Av) * u[10] * shield + + # 7: CHx + du[7] = n_H * (-2e-10) * u[7] * u[8] + + n_H * 4e-16 * u[1] * u[12] + + n_H * 2e-9 * u[2] * u[6] - + 1e-9 * Go * u[7] * exp(-1.5 * Av) + + # 8: O + du[8] = n_H * (-2e-10) * u[7] * u[8] + + n_H * 1.6e-9 * u[10] * u[5] - + n_H * 8e-10 * u[2] * u[8] + + 5e-10 * Go * exp(-1.7 * Av) * u[9] + + 1e-10 * Go * exp(-3 * Av) * u[10] * shield + + # 9: OHx + du[9] = n_H * (-1e-9) * u[9] * u[12] + + n_H * 8e-10 * u[2] * u[8] - + n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - + 5e-10 * Go * exp(-1.7 * Av) * u[9] + + # 10: CO + du[10] = n_H * (3.3e-5 * u[11] * u[3]) / T + + n_H * 2e-10 * u[7] * u[8] - + n_H * 1.7e-9 * u[10] * u[2] - + n_H * 1.6e-9 * u[10] * u[5] + + n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - + 1e-10 * Go * exp(-3 * Av) * u[10] + + 1.5e-10 * Go * exp(-2.5 * Av) * u[11] * shield + + # 11: HCO+ + du[11] = n_H * (-3.3e-5 * u[11] * u[3]) / T + + n_H * 1e-9 * u[9] * u[12] + + n_H * 1.7e-9 * u[10] * u[2] - + 1.5e-10 * Go * exp(-2.5 * Av) * u[11] + + # 12: C+ + du[12] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - + n_H * 4e-16 * u[1] * u[12] - + n_H * 1e-9 * u[9] * u[12] + + n_H * 1.6e-9 * u[10] * u[5] + + 3e-10 * Go * exp(-3 * Av) * u[6] + + # 13: M+ + du[13] = n_H * (-3.8e-10 * u[13] * u[3]) / (T^0.65) + + n_H * 2e-9 * u[2] * u[14] + + 2.0e-10 * Go * exp(-1.9 * Av) * u[14] + + # 14: M + du[14] = n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - + n_H * 2e-9 * u[2] * u[14] - + 2.0e-10 * Go * exp(-1.9 * Av) * u[14] end - -u0 = [0.5 ; # 1: H2 yep? - 9.059e-9 ; # 2: H3+ yep - 2.0e-4 ; # 3: e yep - 0.1 ; # 4: He SEE lines 535 NL99 - 7.866e-7 ; # 5: He+ yep? should be 2.622e-5 - 0.0 ; # 6: C yep - 0.0 ; # 7: CHx yep - 0.0004 ; # 8: O yep - 0.0 ; # 9: OHx yep - 0.0 ; # 10: CO yep - 0.0 ; # 11: HCO+ yep - 0.0002 ; # 12: C+ yep - 2.0e-7 ; # 13: M+ yep - 2.0e-7 ] # 14: M yep - - -tspan = (0.0, 30 * 3.16e10) # ~30 thousand yrs - -prob = ODEProblem(Nelson_ODE, u0, tspan) +# Set the Timespan, Parameters, and Initial Conditions +seconds_per_year = 3600 * 24 * 365 +tspan = (0.0, 30000 * seconds_per_year) # ~30 thousand yrs + +params = (10, # T + 2, # Av + 1.7, # Go + 611, # n_H + 1) # shield + +u0 = [0.5, # 1: H2 + 9.059e-9, # 2: H3+ + 2.0e-4, # 3: e + 0.1, # 4: He + 7.866e-7, # 5: He+ + 0.0, # 6: C + 0.0, # 7: CHx + 0.0004, # 8: O + 0.0, # 9: OHx + 0.0, # 10: CO + 0.0, # 11: HCO+ + 0.0002, # 12: C+ + 2.0e-7, # 13: M+ + 2.0e-7] # 14: M + + +prob = ODEProblem(Nelson!, u0, tspan, params) refsol = solve(prob, Vern9(), abstol=1e-14, reltol=1e-14) +sol2 = solve(prob, FBDF()) +sol3 = solve(prob, QNDF()) +sol4 = solve(prob, CVODE_BDF()) + using Plots -plot(sol; yscale=:log10, idxs = (0,5)) +colors = palette(:acton, 5) +p1 = plot(refsol, vars = (0,11), lc=colors[1], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ Reference solution") +p2 = plot(sol2, vars = (0,11), lc=colors[2], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using FBDF") +p3 = plot(sol3, vars = (0,11), lc=colors[3], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using QNDF") +p4 = plot(sol4, vars = (0,11), lc=colors[4], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using CVODE FBDF") +combined_plot = plot(p1, p2, p3, p4, layout=(4, 1), dpi = 600, pallete=:acton) +display(combined_plot) abstols = 1.0 ./ 10.0 .^ (8:10) reltols = 1.0 ./ 10.0 .^ (8:10) -sol = solve(prob, CVODE_BDF(), abstol=1e-14, reltol=1e-14) setups = [ Dict(:alg=>FBDF()), From 908c271b356e48407837ab1f8976b2858e839bd1 Mon Sep 17 00:00:00 2001 From: Ninadlt <166744945+nnd389@users.noreply.github.com> Date: Thu, 24 Oct 2024 22:10:22 -0500 Subject: [PATCH 5/6] Updated the nelson ODE function, (made it nicer to look at) and added parameters --- dev/AstroChem/nelson/index.html | 288 ++++++++++++++++++-------------- 1 file changed, 160 insertions(+), 128 deletions(-) diff --git a/dev/AstroChem/nelson/index.html b/dev/AstroChem/nelson/index.html index 8b62c0159..e6efd49fe 100644 --- a/dev/AstroChem/nelson/index.html +++ b/dev/AstroChem/nelson/index.html @@ -2,144 +2,176 @@ Nelson Work-Precision Diagrams · The SciML Benchmarks

Nelson Work-Precision Diagrams

using OrdinaryDiffEq
 using DiffEqDevTools, Plots
 using Sundials, LSODA
-using ODEInterface, ODEInterfaceDiffEq
T = 10
-Av = 2 # This is what depotic uses for visual extinction
-Go = 1.7 # I think despotic uses 1.7
-n_H = 611
-shield = 1
-
-function Nelson_ODE(du,u,p,t)
-	# 1: H2
-	#= du[1] = -1.2e-17 * u[1] + 
-			n_H * (1.9e-6 * u[2] * u[3]) / (T^0.54) - 
-			n_H * 4e-16 * u[1] * u[12] - 
-			n_H * 7e-15 * u[1] * u[5] + 
-			n_H * 1.7e-9 * u[10] * u[2] + 
-			n_H * 2e-9 * u[2] * u[6] + 
-			n_H * 2e-9 * u[2] * u[14] + 
-			n_H * 8e-10 * u[2] * u[8] =#
-	du[1] = 0
-
-	# 2: H3+
-	du[2] = 1.2e-17 * u[1] + 
-			n_H * (-1.9e-6 * u[3] * u[2]) / (T^0.54) - 
-			n_H * 1.7e-9 * u[10] * u[2] - 
-			n_H * 2e-9 * u[2] * u[6] - 
-			n_H * 2e-9 * u[2] * u[14] - 
-			n_H * 8e-10 * u[2] * u[8]
-
-	# 3: e
-	du[3] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - 
-			n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - 
-			n_H * (3.3e-5 * u[11] * u[3]) / T + 
-			1.2e-17 * u[1] - 
-			n_H * (1.9e-6 * u[3] * u[2]) / (T^0.54) + 
-			6.8e-18 * u[4] - 
-			n_H * (9e-11 * u[3] * u[5]) / (T^0.64) + 
-			3e-10 * Go * exp(-3 * Av) * u[6] +
-			n_H * 2e-9 * u[2] * u[13] ## CHECK I added this extra term from a CR ionization reaction
-			+ 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction
-	
-	
-	# 4: He
-	du[4] = n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - 
-			6.8e-18 * u[4] + 
-			n_H * 7e-15 * u[1] * u[5] + 
-			n_H * 1.6e-9 * u[10] * u[5]
-	#du[4] = 0
-	
-	# 5: He+   6.8e-18 or 1.1
-	du[5] = 6.8e-18 * u[4] - 
-			n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - 
-			n_H * 7e-15 * u[1] * u[5] - 
-			n_H * 1.6e-9 * u[10] * u[5]
-	#u[5] = 0
-	
-	# 6: C
-	du[6] = n_H * (1.4e-10 * u[3] * u[12]) / (T^0.61) - 
-			n_H * 2e-9 * u[2] * u[6] - 
-			n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] + 
-			1e-9 * Go * exp(-1.5 * Av) * u[7] - 
-			3e-10 * Go * exp(-3 * Av) * u[6] + 
-			1e-10 * Go * exp(-3 * Av) * u[10] * shield
-
-	# 7: CHx
-	du[7] = n_H * (-2e-10) * u[7] * u[8] + 
-			n_H * 4e-16 * u[1] * u[12] + 
-			n_H * 2e-9 * u[2] * u[6] - 
-			1e-9 * Go * u[7] * exp(-1.5 * Av)
-	
-	# 8: O
-	du[8] = n_H * (-2e-10) * u[7] * u[8] + 
-			n_H * 1.6e-9 * u[10] * u[5] - 
-			n_H * 8e-10 * u[2] * u[8] + 
-			5e-10 * Go * exp(-1.7 * Av) * u[9] + 
-			1e-10 * Go * exp(-3 * Av) * u[10] * shield
-	
-	# 9: OHx
-	du[9] = n_H * (-1e-9) * u[9] * u[12] + 
-			n_H * 8e-10 * u[2] * u[8] - 
-			n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - 
-			5e-10 * Go * exp(-1.7 * Av) * u[9]
-
-	# 10: CO
-	du[10] = n_H * (3.3e-5 * u[11] * u[3]) / T + 
-			n_H * 2e-10 * u[7] * u[8] - 
-			n_H * 1.7e-9 * u[10] * u[2] - 
-			n_H * 1.6e-9 * u[10] * u[5] + 
-			n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - 
-			1e-10 * Go * exp(-3 * Av) * u[10] + 
-			1.5e-10 * Go * exp(-2.5 * Av) * u[11] * shield
-	
-	# 11: HCO+
-	du[11] = n_H * (-3.3e-5 * u[11] * u[3]) / T + 
-			n_H * 1e-9 * u[9] * u[12] + 
-			n_H * 1.7e-9 * u[10] * u[2] - 
-			1.5e-10 * Go * exp(-2.5 * Av) * u[11]
-	
-	# 12: C+
-	du[12] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - 
-			n_H * 4e-16 * u[1] * u[12] - 
-			n_H * 1e-9 * u[9] * u[12] + 
-			n_H * 1.6e-9 * u[10] * u[5] + 
-			3e-10 * Go * exp(-3 * Av) * u[6]
-	
-	# 13: M+
-	du[13] = n_H * (-3.8e-10 * u[13] * u[3]) / (T^0.65) + 
-			n_H * 2e-9 * u[2] * u[14] 
-			+ 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction
-	
-	# 14: M
-	du[14] = n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - 
-			n_H * 2e-9 * u[2] * u[14] 
-			- 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction
+using ODEInterface, ODEInterfaceDiffEq

+
+#=
+The ODE function defined below models the reduced carbon-oxygen 
+chemistry network of Nelson & Langer (1999, ApJ, 524, 923).
+
+This Julia ODE function was written by Nina De La Torre advised by Dr. Stella Offner.
+The solution was compared with results derived by DESPOTIC, (Mark Krumholz, 2013) 
+a code to Derive the Energetics and Spectra of Optically Thick Insterstellar Clouds. 
+DESPOTIC has pre-defined networks, one of them coming from the Nelson & Langer paper, 
+so the initial conditions and parameters were meant to mimic those from DESPOTIC.
+
+    Parameter definitions:
+    T = 10     --> Tempurature (Kelvin)
+    Av = 2     --> V-Band Extinction
+    G₀ = 1.7   --> Go; "a factor that determines the flux of FUV radiation relative to the standard interstellar value (G₀ = 1) as reported by Habing (1968)."
+    n_H = 611  --> Hydrogen Number Density
+    shield = 1 --> "CO self-shielding factor of van Dishoeck & Black (1988), taken from Bergin et al. (1995)"
+=#
+
+function Nelson!(du,u,p,t)
+    T, Av, Go, n_H, shield = p
+
+    # 1: H2
+    du[1] = -1.2e-17 * u[1] + 
+            n_H * (1.9e-6 * u[2] * u[3]) / (T^0.54) - 
+            n_H * 4e-16 * u[1] * u[12] - 
+            n_H * 7e-15 * u[1] * u[5] + 
+            n_H * 1.7e-9 * u[10] * u[2] + 
+            n_H * 2e-9 * u[2] * u[6] + 
+            n_H * 2e-9 * u[2] * u[14] + 
+            n_H * 8e-10 * u[2] * u[8] 
+
+    # 2: H3+
+    du[2] = 1.2e-17 * u[1] + 
+            n_H * (-1.9e-6 * u[3] * u[2]) / (T^0.54) - 
+            n_H * 1.7e-9 * u[10] * u[2] - 
+            n_H * 2e-9 * u[2] * u[6] - 
+            n_H * 2e-9 * u[2] * u[14] - 
+            n_H * 8e-10 * u[2] * u[8]
+
+    # 3: e
+    du[3] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - 
+            n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - 
+            n_H * (3.3e-5 * u[11] * u[3]) / T + 
+            1.2e-17 * u[1] - 
+            n_H * (1.9e-6 * u[3] * u[2]) / (T^0.54) + 
+            6.8e-18 * u[4] - 
+            n_H * (9e-11 * u[3] * u[5]) / (T^0.64) + 
+            3e-10 * Go * exp(-3 * Av) * u[6] +
+            n_H * 2e-9 * u[2] * u[13]
+            + 2.0e-10 * Go * exp(-1.9 * Av) * u[14]
+
+    # 4: He
+    du[4] = n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - 
+            6.8e-18 * u[4] + 
+            n_H * 7e-15 * u[1] * u[5] + 
+            n_H * 1.6e-9 * u[10] * u[5]
+
+    # 5: He+
+    du[5] = 6.8e-18 * u[4] - 
+            n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - 
+            n_H * 7e-15 * u[1] * u[5] - 
+            n_H * 1.6e-9 * u[10] * u[5]
+
+    # 6: C
+    du[6] = n_H * (1.4e-10 * u[3] * u[12]) / (T^0.61) - 
+            n_H * 2e-9 * u[2] * u[6] - 
+            n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] + 
+            1e-9 * Go * exp(-1.5 * Av) * u[7] - 
+            3e-10 * Go * exp(-3 * Av) * u[6] + 
+            1e-10 * Go * exp(-3 * Av) * u[10] * shield
+
+    # 7: CHx
+    du[7] = n_H * (-2e-10) * u[7] * u[8] + 
+            n_H * 4e-16 * u[1] * u[12] + 
+            n_H * 2e-9 * u[2] * u[6] - 
+            1e-9 * Go * u[7] * exp(-1.5 * Av)
+
+    # 8: O
+    du[8] = n_H * (-2e-10) * u[7] * u[8] + 
+            n_H * 1.6e-9 * u[10] * u[5] - 
+            n_H * 8e-10 * u[2] * u[8] + 
+            5e-10 * Go * exp(-1.7 * Av) * u[9] + 
+            1e-10 * Go * exp(-3 * Av) * u[10] * shield
+
+    # 9: OHx
+    du[9] = n_H * (-1e-9) * u[9] * u[12] + 
+            n_H * 8e-10 * u[2] * u[8] - 
+            n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - 
+            5e-10 * Go * exp(-1.7 * Av) * u[9]
+
+    # 10: CO
+    du[10] = n_H * (3.3e-5 * u[11] * u[3]) / T + 
+             n_H * 2e-10 * u[7] * u[8] - 
+             n_H * 1.7e-9 * u[10] * u[2] - 
+             n_H * 1.6e-9 * u[10] * u[5] + 
+             n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - 
+             1e-10 * Go * exp(-3 * Av) * u[10] + 
+             1.5e-10 * Go * exp(-2.5 * Av) * u[11] * shield
+
+    # 11: HCO+
+    du[11] = n_H * (-3.3e-5 * u[11] * u[3]) / T + 
+             n_H * 1e-9 * u[9] * u[12] + 
+             n_H * 1.7e-9 * u[10] * u[2] - 
+             1.5e-10 * Go * exp(-2.5 * Av) * u[11]
+
+    # 12: C+
+    du[12] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - 
+             n_H * 4e-16 * u[1] * u[12] - 
+             n_H * 1e-9 * u[9] * u[12] + 
+             n_H * 1.6e-9 * u[10] * u[5] + 
+             3e-10 * Go * exp(-3 * Av) * u[6]
+
+    # 13: M+
+    du[13] = n_H * (-3.8e-10 * u[13] * u[3]) / (T^0.65) + 
+             n_H * 2e-9 * u[2] * u[14] +
+             2.0e-10 * Go * exp(-1.9 * Av) * u[14]
+
+    # 14: M
+    du[14] = n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - 
+             n_H * 2e-9 * u[2] * u[14] -
+             2.0e-10 * Go * exp(-1.9 * Av) * u[14]
 
 end
 
+# Set the Timespan, Parameters, and Initial Conditions
+seconds_per_year = 3600 * 24 * 365
+tspan = (0.0, 30000 * seconds_per_year) # ~30 thousand yrs
 
-u0 = [0.5 ;    # 1:  H2   yep?
-	9.059e-9 ; # 2:  H3+  yep
-	2.0e-4 ;   # 3:  e    yep
-	0.1 ;              # 4:  He  SEE lines 535 NL99
-	7.866e-7 ; # 5:  He+  yep? should be 2.622e-5
-	0.0 ;      # 6:  C    yep
-	0.0 ;      # 7:  CHx  yep
-	0.0004 ;   # 8:  O    yep
-	0.0 ;      # 9:  OHx  yep
-	0.0 ;      # 10: CO   yep
-	0.0 ;      # 11: HCO+ yep
-	0.0002 ;   # 12: C+   yep
-	2.0e-7 ;   # 13: M+   yep
-	2.0e-7 ]   # 14: M    yep
+params = (10,  # T
+          2,   # Av
+          1.7, # Go
+          611, # n_H
+          1)   # shield
 
+u0 = [0.5,      # 1:  H2
+      9.059e-9, # 2:  H3+
+      2.0e-4,   # 3:  e
+      0.1,      # 4:  He
+      7.866e-7, # 5:  He+
+      0.0,      # 6:  C
+      0.0,      # 7:  CHx
+      0.0004,   # 8:  O
+      0.0,      # 9:  OHx
+      0.0,      # 10: CO
+      0.0,      # 11: HCO+
+      0.0002,   # 12: C+
+      2.0e-7,   # 13: M+
+      2.0e-7]   # 14: M
 
-tspan = (0.0, 30 * 3.16e10) # ~30 thousand yrs
 
-prob = ODEProblem(Nelson_ODE, u0, tspan)
+prob = ODEProblem(Nelson!, u0, tspan, params)
 refsol = solve(prob, Vern9(), abstol=1e-14, reltol=1e-14)
+sol2 = solve(prob, FBDF())
+sol3 = solve(prob, QNDF())
+sol4 = solve(prob, CVODE_BDF())
+
 
 using Plots
-plot(sol; yscale=:log10, idxs = (0,5))
Error: UndefVarError: `sol` not defined

Run Benchmark

abstols = 1.0 ./ 10.0 .^ (8:10)
+colors = palette(:acton, 5)
+p1 = plot(refsol, vars = (0,11), lc=colors[1], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ Reference solution")
+p2 = plot(sol2,   vars = (0,11), lc=colors[2], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using FBDF")
+p3 = plot(sol3,   vars = (0,11), lc=colors[3], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using QNDF")
+p4 = plot(sol4,   vars = (0,11), lc=colors[4], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using CVODE FBDF")
+combined_plot = plot(p1, p2, p3, p4, layout=(4, 1), dpi = 600, pallete=:acton)
+display(combined_plot)
+	
+
+

Run Benchmark

abstols = 1.0 ./ 10.0 .^ (8:10)
 reltols = 1.0 ./ 10.0 .^ (8:10)
 
 sol = solve(prob, CVODE_BDF(), abstol=1e-14, reltol=1e-14)

From bbcdd64b9561783582b567b6511b29adfe555f7b Mon Sep 17 00:00:00 2001
From: Ninadlt <166744945+nnd389@users.noreply.github.com>
Date: Thu, 24 Oct 2024 22:11:38 -0500
Subject: [PATCH 6/6] Update index.html

---
 v0.6/AstroChem/nelson/index.html | 289 +++++++++++++++++--------------
 1 file changed, 159 insertions(+), 130 deletions(-)

diff --git a/v0.6/AstroChem/nelson/index.html b/v0.6/AstroChem/nelson/index.html
index 8fa48b928..09fa8cb32 100644
--- a/v0.6/AstroChem/nelson/index.html
+++ b/v0.6/AstroChem/nelson/index.html
@@ -2,148 +2,177 @@
 Nelson Work-Precision Diagrams · The SciML Benchmarks

Nelson Work-Precision Diagrams

using OrdinaryDiffEq
 using DiffEqDevTools, Plots
 using Sundials, LSODA
-using ODEInterface, ODEInterfaceDiffEq
T = 10
-Av = 2 # This is what depotic uses for visual extinction
-Go = 1.7 # I think despotic uses 1.7
-n_H = 611
-shield = 1
-
-function Nelson_ODE(du,u,p,t)
-	# 1: H2
-	#= du[1] = -1.2e-17 * u[1] + 
-			n_H * (1.9e-6 * u[2] * u[3]) / (T^0.54) - 
-			n_H * 4e-16 * u[1] * u[12] - 
-			n_H * 7e-15 * u[1] * u[5] + 
-			n_H * 1.7e-9 * u[10] * u[2] + 
-			n_H * 2e-9 * u[2] * u[6] + 
-			n_H * 2e-9 * u[2] * u[14] + 
-			n_H * 8e-10 * u[2] * u[8] =#
-	du[1] = 0
-
-	# 2: H3+
-	du[2] = 1.2e-17 * u[1] + 
-			n_H * (-1.9e-6 * u[3] * u[2]) / (T^0.54) - 
-			n_H * 1.7e-9 * u[10] * u[2] - 
-			n_H * 2e-9 * u[2] * u[6] - 
-			n_H * 2e-9 * u[2] * u[14] - 
-			n_H * 8e-10 * u[2] * u[8]
-
-	# 3: e
-	du[3] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - 
-			n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - 
-			n_H * (3.3e-5 * u[11] * u[3]) / T + 
-			1.2e-17 * u[1] - 
-			n_H * (1.9e-6 * u[3] * u[2]) / (T^0.54) + 
-			6.8e-18 * u[4] - 
-			n_H * (9e-11 * u[3] * u[5]) / (T^0.64) + 
-			3e-10 * Go * exp(-3 * Av) * u[6] +
-			n_H * 2e-9 * u[2] * u[13] ## CHECK I added this extra term from a CR ionization reaction
-			+ 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction
-	
-	
-	# 4: He
-	du[4] = n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - 
-			6.8e-18 * u[4] + 
-			n_H * 7e-15 * u[1] * u[5] + 
-			n_H * 1.6e-9 * u[10] * u[5]
-	#du[4] = 0
-	
-	# 5: He+   6.8e-18 or 1.1
-	du[5] = 6.8e-18 * u[4] - 
-			n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - 
-			n_H * 7e-15 * u[1] * u[5] - 
-			n_H * 1.6e-9 * u[10] * u[5]
-	#u[5] = 0
-	
-	# 6: C
-	du[6] = n_H * (1.4e-10 * u[3] * u[12]) / (T^0.61) - 
-			n_H * 2e-9 * u[2] * u[6] - 
-			n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] + 
-			1e-9 * Go * exp(-1.5 * Av) * u[7] - 
-			3e-10 * Go * exp(-3 * Av) * u[6] + 
-			1e-10 * Go * exp(-3 * Av) * u[10] * shield
-
-	# 7: CHx
-	du[7] = n_H * (-2e-10) * u[7] * u[8] + 
-			n_H * 4e-16 * u[1] * u[12] + 
-			n_H * 2e-9 * u[2] * u[6] - 
-			1e-9 * Go * u[7] * exp(-1.5 * Av)
-	
-	# 8: O
-	du[8] = n_H * (-2e-10) * u[7] * u[8] + 
-			n_H * 1.6e-9 * u[10] * u[5] - 
-			n_H * 8e-10 * u[2] * u[8] + 
-			5e-10 * Go * exp(-1.7 * Av) * u[9] + 
-			1e-10 * Go * exp(-3 * Av) * u[10] * shield
-	
-	# 9: OHx
-	du[9] = n_H * (-1e-9) * u[9] * u[12] + 
-			n_H * 8e-10 * u[2] * u[8] - 
-			n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - 
-			5e-10 * Go * exp(-1.7 * Av) * u[9]
-
-	# 10: CO
-	du[10] = n_H * (3.3e-5 * u[11] * u[3]) / T + 
-			n_H * 2e-10 * u[7] * u[8] - 
-			n_H * 1.7e-9 * u[10] * u[2] - 
-			n_H * 1.6e-9 * u[10] * u[5] + 
-			n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - 
-			1e-10 * Go * exp(-3 * Av) * u[10] + 
-			1.5e-10 * Go * exp(-2.5 * Av) * u[11] * shield
-	
-	# 11: HCO+
-	du[11] = n_H * (-3.3e-5 * u[11] * u[3]) / T + 
-			n_H * 1e-9 * u[9] * u[12] + 
-			n_H * 1.7e-9 * u[10] * u[2] - 
-			1.5e-10 * Go * exp(-2.5 * Av) * u[11]
-	
-	# 12: C+
-	du[12] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - 
-			n_H * 4e-16 * u[1] * u[12] - 
-			n_H * 1e-9 * u[9] * u[12] + 
-			n_H * 1.6e-9 * u[10] * u[5] + 
-			3e-10 * Go * exp(-3 * Av) * u[6]
-	
-	# 13: M+
-	du[13] = n_H * (-3.8e-10 * u[13] * u[3]) / (T^0.65) + 
-			n_H * 2e-9 * u[2] * u[14] 
-			+ 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction
-	
-	# 14: M
-	du[14] = n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - 
-			n_H * 2e-9 * u[2] * u[14] 
-			- 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction
+using ODEInterface, ODEInterfaceDiffEq

+
+#=
+The ODE function defined below models the reduced carbon-oxygen 
+chemistry network of Nelson & Langer (1999, ApJ, 524, 923).
+
+This Julia ODE function was written by Nina De La Torre advised by Dr. Stella Offner.
+The solution was compared with results derived by DESPOTIC, (Mark Krumholz, 2013) 
+a code to Derive the Energetics and Spectra of Optically Thick Insterstellar Clouds. 
+DESPOTIC has pre-defined networks, one of them coming from the Nelson & Langer paper, 
+so the initial conditions and parameters were meant to mimic those from DESPOTIC.
+
+    Parameter definitions:
+    T = 10     --> Tempurature (Kelvin)
+    Av = 2     --> V-Band Extinction
+    G₀ = 1.7   --> Go; "a factor that determines the flux of FUV radiation relative to the standard interstellar value (G₀ = 1) as reported by Habing (1968)."
+    n_H = 611  --> Hydrogen Number Density
+    shield = 1 --> "CO self-shielding factor of van Dishoeck & Black (1988), taken from Bergin et al. (1995)"
+=#
+
+function Nelson!(du,u,p,t)
+    T, Av, Go, n_H, shield = p
+
+    # 1: H2
+    du[1] = -1.2e-17 * u[1] + 
+            n_H * (1.9e-6 * u[2] * u[3]) / (T^0.54) - 
+            n_H * 4e-16 * u[1] * u[12] - 
+            n_H * 7e-15 * u[1] * u[5] + 
+            n_H * 1.7e-9 * u[10] * u[2] + 
+            n_H * 2e-9 * u[2] * u[6] + 
+            n_H * 2e-9 * u[2] * u[14] + 
+            n_H * 8e-10 * u[2] * u[8] 
+
+    # 2: H3+
+    du[2] = 1.2e-17 * u[1] + 
+            n_H * (-1.9e-6 * u[3] * u[2]) / (T^0.54) - 
+            n_H * 1.7e-9 * u[10] * u[2] - 
+            n_H * 2e-9 * u[2] * u[6] - 
+            n_H * 2e-9 * u[2] * u[14] - 
+            n_H * 8e-10 * u[2] * u[8]
+
+    # 3: e
+    du[3] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - 
+            n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - 
+            n_H * (3.3e-5 * u[11] * u[3]) / T + 
+            1.2e-17 * u[1] - 
+            n_H * (1.9e-6 * u[3] * u[2]) / (T^0.54) + 
+            6.8e-18 * u[4] - 
+            n_H * (9e-11 * u[3] * u[5]) / (T^0.64) + 
+            3e-10 * Go * exp(-3 * Av) * u[6] +
+            n_H * 2e-9 * u[2] * u[13]
+            + 2.0e-10 * Go * exp(-1.9 * Av) * u[14]
+
+    # 4: He
+    du[4] = n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - 
+            6.8e-18 * u[4] + 
+            n_H * 7e-15 * u[1] * u[5] + 
+            n_H * 1.6e-9 * u[10] * u[5]
+
+    # 5: He+
+    du[5] = 6.8e-18 * u[4] - 
+            n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - 
+            n_H * 7e-15 * u[1] * u[5] - 
+            n_H * 1.6e-9 * u[10] * u[5]
+
+    # 6: C
+    du[6] = n_H * (1.4e-10 * u[3] * u[12]) / (T^0.61) - 
+            n_H * 2e-9 * u[2] * u[6] - 
+            n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] + 
+            1e-9 * Go * exp(-1.5 * Av) * u[7] - 
+            3e-10 * Go * exp(-3 * Av) * u[6] + 
+            1e-10 * Go * exp(-3 * Av) * u[10] * shield
+
+    # 7: CHx
+    du[7] = n_H * (-2e-10) * u[7] * u[8] + 
+            n_H * 4e-16 * u[1] * u[12] + 
+            n_H * 2e-9 * u[2] * u[6] - 
+            1e-9 * Go * u[7] * exp(-1.5 * Av)
+
+    # 8: O
+    du[8] = n_H * (-2e-10) * u[7] * u[8] + 
+            n_H * 1.6e-9 * u[10] * u[5] - 
+            n_H * 8e-10 * u[2] * u[8] + 
+            5e-10 * Go * exp(-1.7 * Av) * u[9] + 
+            1e-10 * Go * exp(-3 * Av) * u[10] * shield
+
+    # 9: OHx
+    du[9] = n_H * (-1e-9) * u[9] * u[12] + 
+            n_H * 8e-10 * u[2] * u[8] - 
+            n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - 
+            5e-10 * Go * exp(-1.7 * Av) * u[9]
+
+    # 10: CO
+    du[10] = n_H * (3.3e-5 * u[11] * u[3]) / T + 
+             n_H * 2e-10 * u[7] * u[8] - 
+             n_H * 1.7e-9 * u[10] * u[2] - 
+             n_H * 1.6e-9 * u[10] * u[5] + 
+             n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - 
+             1e-10 * Go * exp(-3 * Av) * u[10] + 
+             1.5e-10 * Go * exp(-2.5 * Av) * u[11] * shield
+
+    # 11: HCO+
+    du[11] = n_H * (-3.3e-5 * u[11] * u[3]) / T + 
+             n_H * 1e-9 * u[9] * u[12] + 
+             n_H * 1.7e-9 * u[10] * u[2] - 
+             1.5e-10 * Go * exp(-2.5 * Av) * u[11]
+
+    # 12: C+
+    du[12] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - 
+             n_H * 4e-16 * u[1] * u[12] - 
+             n_H * 1e-9 * u[9] * u[12] + 
+             n_H * 1.6e-9 * u[10] * u[5] + 
+             3e-10 * Go * exp(-3 * Av) * u[6]
+
+    # 13: M+
+    du[13] = n_H * (-3.8e-10 * u[13] * u[3]) / (T^0.65) + 
+             n_H * 2e-9 * u[2] * u[14] +
+             2.0e-10 * Go * exp(-1.9 * Av) * u[14]
+
+    # 14: M
+    du[14] = n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - 
+             n_H * 2e-9 * u[2] * u[14] -
+             2.0e-10 * Go * exp(-1.9 * Av) * u[14]
 
 end
 
+# Set the Timespan, Parameters, and Initial Conditions
+seconds_per_year = 3600 * 24 * 365
+tspan = (0.0, 30000 * seconds_per_year) # ~30 thousand yrs
 
-u0 = [0.5 ;    # 1:  H2   yep?
-	9.059e-9 ; # 2:  H3+  yep
-	2.0e-4 ;   # 3:  e    yep
-	0.1 ;              # 4:  He  SEE lines 535 NL99
-	7.866e-7 ; # 5:  He+  yep? should be 2.622e-5
-	0.0 ;      # 6:  C    yep
-	0.0 ;      # 7:  CHx  yep
-	0.0004 ;   # 8:  O    yep
-	0.0 ;      # 9:  OHx  yep
-	0.0 ;      # 10: CO   yep
-	0.0 ;      # 11: HCO+ yep
-	0.0002 ;   # 12: C+   yep
-	2.0e-7 ;   # 13: M+   yep
-	2.0e-7 ]   # 14: M    yep
+params = (10,  # T
+          2,   # Av
+          1.7, # Go
+          611, # n_H
+          1)   # shield
 
+u0 = [0.5,      # 1:  H2
+      9.059e-9, # 2:  H3+
+      2.0e-4,   # 3:  e
+      0.1,      # 4:  He
+      7.866e-7, # 5:  He+
+      0.0,      # 6:  C
+      0.0,      # 7:  CHx
+      0.0004,   # 8:  O
+      0.0,      # 9:  OHx
+      0.0,      # 10: CO
+      0.0,      # 11: HCO+
+      0.0002,   # 12: C+
+      2.0e-7,   # 13: M+
+      2.0e-7]   # 14: M
 
-tspan = (0.0, 30 * 3.16e10) # ~30 thousand yrs
 
-prob = ODEProblem(Nelson_ODE, u0, tspan)
+prob = ODEProblem(Nelson!, u0, tspan, params)
 refsol = solve(prob, Vern9(), abstol=1e-14, reltol=1e-14)
+sol2 = solve(prob, FBDF())
+sol3 = solve(prob, QNDF())
+sol4 = solve(prob, CVODE_BDF())
+
 
 using Plots
-plot(sol; yscale=:log10, idxs = (0,5))
Error: UndefVarError: `sol` not defined

Run Benchmark

abstols = 1.0 ./ 10.0 .^ (8:10)
+colors = palette(:acton, 5)
+p1 = plot(refsol, vars = (0,11), lc=colors[1], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ Reference solution")
+p2 = plot(sol2,   vars = (0,11), lc=colors[2], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using FBDF")
+p3 = plot(sol3,   vars = (0,11), lc=colors[3], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using QNDF")
+p4 = plot(sol4,   vars = (0,11), lc=colors[4], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using CVODE FBDF")
+combined_plot = plot(p1, p2, p3, p4, layout=(4, 1), dpi = 600, pallete=:acton)
+display(combined_plot)
+	
+

Run Benchmark

abstols = 1.0 ./ 10.0 .^ (8:10)
 reltols = 1.0 ./ 10.0 .^ (8:10)
 
-sol = solve(prob, CVODE_BDF(), abstol=1e-14, reltol=1e-14)
-
 setups = [
           Dict(:alg=>FBDF()),
           Dict(:alg=>QNDF()),