AMS 528, Numerical Methods for PDEs

Introduction to key concepts and algorithms for finding numerical solutions to partial differential equations (PDEs). Topics include analysis of consistency, stability and convergence, and finite difference and/or finite volume methods for the three major classes of PDEs: parabolic, elliptic, and hyperbolic. Practical implementations, important packages of scientific software algorithms, and examples of modern scientific and engineering applications are also discussed.

Co-requisite:  AMS 502
3 credits, ABCF grading
Spring semesters

Required Texts:

Numerical Partial Differential Equations: Finite Difference Methods (TAM 22), by J.W. Thomas, Springer (1995), Volume I; ISBN 0-387-97999-1

Numerical Methods for Conservation Laws, by Randall J. LeVeque, 2nd edition, Birkhauser Verlag, 1992, ISBN 978-376-4-32723-1

AMS 528 Instructor Page

Learning Outcomes:

1) Demonstrate mastery of: 
      * Finite difference methods for PDE;
      * Consistency, convergence and stability, Lax theorem;
      * Parabolic equations, implicit schemes, convection diffusion equations;
      * Two dimensional problems, alternate directional implicit (ADI);
      * Hyperbolic equations, numerical schemes, stability analysis and CFL condition;
      * Numerical dispersion and numerical dissipation, tracking and capturing;
      * Conservation Law, Glimm scheme and Godunov scheme, high order schemes, limiters;
      * Elliptic equations, iterative methods;
      * Introduction to the finite element method;
      * Meshless and particle methods for PDE's.