Fix

jointContribution/PIRBN/README.md

@@ -13,44 +13,11 @@ Inspired by findings, we proposed the PIRBN, which can exhibit the local propert
 
 Numerical examples include:
 
- - 1D sine funtion (**Eq. 15** in the manuscript)
+ - 1D sine funtion (**Eq. 1** in the manuscript)
 
-      **PDE**: $\frac{\partial^2 }{\partial x^2}u(x-100)-4\mu^2\pi^2 sin(2\mu\pi(x-100))=0, x\in[100,101]$
+      **PDE**: $\frac{\partial^2 }{\partial x^2}u(x)-4\mu^2\pi^2 sin(2\mu\pi(x))=0, x\in[0,1]$
 
-      **BC**:  $u(100)=u(101)=0.$
-
- - 1D sine function coupling problem (**Eq. 30** in the manuscript)
-
-      **PDE**: $\frac{\partial^2 }{\partial x^2}u(x)=f(x), x\in[20,22]$
-
-      **BC**:  $u(20)=u(22)=0.$
-
- - 1D nonlinear spring equation (**Eq. 31** in the manuscript)
-
-      **PDE**: $\frac{\partial^2 }{\partial x^2}u(x)+4u(x)+sin[u(x)]=f(x), x\in[0,100]$
-
-      **BC**:  $u(0)=\frac{\partial }{\partial x}u(0)=0.$
-
- - 2D wave equation (**Eq. 33** in the manuscript)
-
-      **PDE**: $(\frac{\partial^2 }{\partial x^2}+4\frac{\partial^2 }{\partial y^2})u(x,y)=0, x\in[0,1], y\in[0,1]$
-
-      **BC**:  $u(x,0)=u(x,1)=\frac{\partial }{\partial x}u(0,y)=0,$
-               $u(0,y)=sin(\pi y)+0.5sin(4\pi y).$
-
- - 2D diffusion equation (**Eq. 35** in the manuscript)
-
-      **PDE**: $(\frac{\partial}{\partial t}-0.01\frac{\partial^2 }{\partial x^2})u(x,t)=g(x,t), x\in[5,10], y\in[5,10]$
-
-      **BC\IC**:  $u(5,t)=b_1(t),u(10,t)=b_2(t),u(x,5)=b_3(x).$
-
- - 2D viscoelastic Poiseuille problem (**Eq. 37** in the manuscript)
-
-      **PDEs**: $\rho\frac{\partial}{\partial t}u(y,t)=-f+\frac{\partial}{\partial y}\tau_{xy}(y,t), t\in[0,4],$  
-                $\eta_0\frac{\partial}{\partial y}u(y,t)=(\lambda\frac{\partial}{\partial t}+1)\tau_{xy}(y,t), y\in[0,1],$
-
-      **BC\IC**:  $u(\pm0.5,t)=u(y,0)=0,$
-                $\tau(y,0)=0.$
+      **BC**:  $u(0)=u(1)=0.$
 
 For more details in terms of mathematical proofs and numerical examples, please refer to our paper.