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 6 Hyperbolic Equations

Pp. 125-147 (23)

Tadeusz Stys

Abstract

In chapter 6, the finite difference scheme with weight 0 ≤ σ ≤ 1 has been built for the wave equation with initial boundary value conditions. It is proved that the scheme is convergent and the global error estimate is given. The scheme with weight  is solved by the method of separation of variables. The Mathematica module waveEqn is designed and applied to initial boundary value problems for the wave equation. In the last section, the wave equation is solved by the method of lines. The chapter ends with a set of questions.

Affiliation:

University of Warsaw.