Difference between revisions of "Math 511: Numerical Methods for PDEs"
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Recall the CFL condition its relation with stability; | Recall the CFL condition its relation with stability; |
Revision as of 12:35, 19 October 2010
Contents
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):