Wave Equations Stability

This lecture covers the analysis of resonant shallow water equations, von Neumann stability analysis, variable phase speed (tsunami), stability limit CFL, explicit diagram with 3 levels, WKB approximation, and demonstrations on eigenmodes, eigenfrequencies, and excitation. The instructor explains the separation of variables, eigenvalues, natural modes and frequencies, and the superposition principle. The lecture also delves into the conditions for the superposition of eigenfunctions and the search for clean modes in waves, emphasizing the importance of stability in the finite difference scheme.