PDEs

1. PDEs Solver(Partial Differential Equations Solver)

The coverage of these problems is:

• Wave equation using Finite-Difference method.

  $\frac{\partial^2 U(x,t)}{\partial t^2}=c^2\frac{\partial^2 U(x,t)}{\partial x^2}$

• Heat equation using Forward-Difference method.

  $\frac{\partial U(x,t)}{\partial t}=c^2\frac{\partial^2 U(x,t)}{\partial x^2}$

• Laplace's equation using Dirichlet method.

  $\frac{\partial^2 U(x,y)}{\partial x^2}+\frac{\partial^2 U(x,y)}{\partial y^2}=0$

• Poisson's equation using Finite-Difference method.

  $\frac{\partial^2 U(x,y)}{\partial x^2}+\frac{\partial^2 U(x,y)}{\partial y^2}=F(x,y)$

This app build in Visual Studio 2017 CE.
Use libraries :

1. mXparser(free version/NON-COMMERCIAL USE) by Mariusz Gromada as math expression parser.
2. ProEssentials Gigasoft(free version/evaluating) for Viewing graph 3D.
   Download sourcecode and app on: https://github.com/nix97/PDEs/releases/download/PDE/PDEs.Solver.zip
   
   

2. Wave Equation

Wave equation using Finite-Difference method.

$\frac{\partial^2 U(x,t)}{\partial t^2}=c^2\frac{\partial^2 U(x,t)}{\partial x^2}$

This app build in Matlab 2016a(GUI version).
Download sourcecode on:
https://github.com/nix97/PDEs/releases/download/PDE2/Wave.Equation.zip

3. Wave Equation py

Wave equation using Finite-Difference method.

$\frac{\partial^2 U(x,t)}{\partial t^2}=c^2\frac{\partial^2 U(x,t)}{\partial x^2}$

This app build in PyCharm 2022 CE.
Use lib:
1. pymep as math parser to input math equation at runtime.
2. plotly as 3D(Surface) graph to display on browser.