MTH693A - Numerical Solution Of Partial Differential Equations

Basic linear algebra vector and matrix norms and related theorems. Parabolic equations in one and two space dimensions explicit and implicit formulae. Consistency, stability and convergence. Iterative methods for linear systems. Split operator methods. Multilevel difference schemes. Nonlinear equations. Elliptic Equations Dirichlet, Neumann and mixed problems. Direct factorization methods and successive over relaxation (S.O.R.). ADI and conjugate gradient methods. Hyperbolic equations. First order hyperbolic systems in one and two space dimensions stability and convergence. Second order equations in one and two space dimensions. The Galerkin method and applications.