 
Summary: MATH 8445, University of Minnesota
Numerical Analysis of Differential Equations
Lecture notes on
Numerical Analysis of
Partial Differential Equations
version of 20110905
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 5point difference operator 7
2. Analysis via a maximum principle 10
3. Consistency, stability, and convergence 11
4. Fourier analysis 13
