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Summary: MATH 8445, University of Minnesota, Fall 2009
Numerical Analysis of Differential Equations
Instructor's notes
Douglas N. Arnold
c 2009 by Douglas N. Arnold. These notes may not be duplicated without explicit permission from the author.
Contents
Chapter 1. Introduction 1
1. Basic examples of PDEs 1
1.1. Heat flow and the heat equation 1
1.2. Elastic membranes 3
1.3. Elastic plates 3
2. Some motivations for studying the numerical analysis of PDE 4
Chapter 2. The finite difference method for the Laplacian 7
1. The 5-point difference operator 7
2. Analysis via a maximum principle 10
3. Consistency, stability, and convergence 11
4. Fourier analysis 13
5. Analysis via summation by parts 15
6. Extensions 17
6.1. Curved boundaries 17
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