Lecture Notes in Numerical Methods of Differential Equations

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This Ebook is designed for science and engineering students taking a course in numerical methods of differential equations. Most of the material in this Ebook has its origin based on lecture courses ...
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Chapter 3 Finite Difference Method

Pp. 55-77 (23)

Tadeusz Stys

Abstract

Two techniques of analysis of convergence and the global error estimates have been developed. The first technique is based on the discrete maximum principle to prove uniform con- vergence of finite difference methods for elliptic and parabolic equations. The second technique draws on spectral analysis and deals with average convergence in the discrete Hilbert’s space H. The chapter ends with a set of questions.

Affiliation:

University of Warsaw.