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: |