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scientific-computing-algorithms

This repo stores my revision and implementations of numerical methods in mathematics (written in Python), including:

  • Differentiation
    • Forward difference
    • Backward difference
    • Central difference
    • Source file: Python
  • Root finding
    • Bisection method
    • Newton's method
    • Secant method
    • Source file: Python
  • Integration
    • Midpoint rule
    • Trapezoidal rule
    • Simpson's rule
    • Adaptive integration, e.g. quad.m in MATLAB
    • Source file: Python
  • Differential equations
    • Euler method
    • Modified Euler method
    • Midpoint method
    • Second-order Runge-Kutta methods
    • Fourth-order Runge-Kutta methods
    • Source file: Python
  • And More!

Targets

To finish this repo, I will implement the numerical methods suggested in the reference, and also to make notes on different topics. Apart from the references, I would also like to include some topics that I have hands-on expereience during my research studies. For example:

  • Mathematical optimization
  • Kalman filtering
  • Structural dynamics
  • Bayesian model updating

References

Lecture Notes on Scientific Computing (Harvey Mudd College, Math 164). Prof. Jeffrey R. CHASNOV. HKUST.

Mathematical Python. Dr. Patrick Walls. UBC.