Course description of AM213B

AM213B focuses on the theory and computer implementation of numerical methods for solving differential equations (ODEs and PDEs) The topics include

• Numerical methods for solving ODEs: Initial value problems using Single-step methods (Euler method, Runge-Kutta methods) and Multi-step methods. Error analysis (Local truncation error, discretization error, roundoff error, global error). Stiff ODE systems. Predictor-corrector method, extrapolation method. Boundary value problems (Finite difference, shooting methods).

• Numerical methods for solving PDEs: Finite difference methods for hyperbolic PDEs (upwind, Lax-Friedrich, Lax-Wendroff methods), finite difference methods for parabolic PDEs (explicit and Crank-Nicolson methods), finite difference methods for elliptic PDEs (direct methods and iterative methods). Dispersion and diffusion errors. Consistency, stability and convergence, von Neumann stability analysis. Lax Equivalence Theorem. CFL condition.