Finite Differences: Partial Differential Equations
Consider the 1D wave equation:
Like most of these problems, I like to visualize what's going on and arrive at an intuitive interpretation of an equation, in this case, the wave equation:
Write down the straightforward finite-difference approximation.
What order approximation is this in time and in space?
Use the von Neumann stability crtierion to find the mode amplitudes:
Numerically solve the wave equation. Using Mathematica: