Difference between revisions of "Math 511: Numerical Methods for PDEs"

Revision as of 12:35, 19 October 2010

Catalog Information

Title

Numerical Methods for Partial Differential Equations.

Credit Hours

3

Prerequisite

Math 303 or 347; 410; or equivalents.

Description

Finite difference and finite volume methods for partial differential equations. Stability, consistency, and convergence theory.

Desired Learning Outcomes

Prerequisites

Minimal learning outcomes

Derive finite difference schemes using Taylor series;

Determine the consistency of a difference scheme;

Explain the proper function spaces and discrete norms for grid functions for use in analysis of stability;

Establish the stability of a difference scheme using (1) Heuristic approach (2) Energy method (3) von Neumann method (4) Matrix method;

Recall the CFL condition its relation with stability;

Explain the convergence of the finite difference approximations and its relation with consistency and stability via Lax theorem;

Determine the order of accuracy of a finite difference scheme;

Implement finite difference schemes on computers and perform numerical studies of the stability and convergence properties of the schemes;

Explain the role and the control of numerical diffusion and dispersion in computation ; to determine how numerical phase speed and group velocity may deviate from the theoretical phase speed and group velocity and the numerical techniques to handle such issues;

Recall numerical methods that efficiently handle a multidimensional problem

Recall alternating direction methods that reduce higher dimensional problems into a sequence of one dimensional problems.

Recall the maximum principles for numerical schemes for Laplace equations;

Recall iterative techniques for solving the linear systems resulting from finite element discretization;

Textbooks

Possible textbooks for this course include (but are not limited to):

Additional topics

Courses for which this course is prerequisite