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Unformatted text preview: APMA E4301x: Numerical Methods for Partial Differential Equations OFFICIAL COURSE DESCRIPTION (FROM THE 2007-2008 BULLETIN): Numerical solution of partial differential equations (PDE) arising in various physical fields of application. Finite difference, finite element, and spectral methods. Elementary finite volume methods for conservation laws. Time stepping, method of lines, and simultaneous space-time discretization. Direct and iterative methods for boundary-value problems. Applied numerical analysis of PDE, including sources of numerical error and notions of convergence and stability, to an extent necessary for successful numerical modeling of physical phenomena. Applications will include the Poisson equation, heat equation, wave equation, and nonlinear equations of fluid, solid, and gas dynamics. Homework assignments will involve substantial programming. MOTIVATION Simulations based on discretizations of partial differential equations (PDEs) are ubiquitous in science and engineering. We shall construct and characterize the behavior of computational methods for PDEs based onengineering....
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This note was uploaded on 08/30/2011 for the course APMA 4301 taught by Professor Keyes during the Fall '08 term at Columbia.
- Fall '08