I have been working on a program for teaching and research on One Dimensional Partial Differential Equation Numerical Solution Methods. I hope to add many more methods and PDE equations. The current Wave and Burger's Equation solvers with symmetric boundary conditions can be fun to play with various parameters. The figure below shows solutions using three different solvers at a CFL of 0.9. CFL is a time step constraint where at a CFL of 1 the wave would travel one point each step. The methods shown are 1st order upwind Euler explicit which is dissipative so the amplitude decreases. The FEM, Finite Element Method, uses the very stable trapezoidal time integration with linear elements. This FEM method has no dissipation but some phase error resulting in a shift in the peak values. Finally the RK4 - Fourth order Runge Kutta method using FEM linear elements is the most accurate but requires more computation and is stable only to CFL = 1.
PDE1D screen shot.
