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Numerical solution of a time-like Cauchy problem for the wave equation

✍ Scribed by Michael Klibanov; Rakesh

Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
415 KB
Volume
15
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

Let D βŠ‚ ℝ^n^ be a bounded domain with piecewise‐smooth boundary, and q(x,t) a smooth function on D Γ— [0, T]. Consider the time‐like Cauchy problem
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Given g, h for which the equation has a solution, we show how to approximate u(x,t) by solving a well posed fourth‐order elliptic partial differential equation (PDE). We use the method of quasi‐reversibility to construct the approximating PDE. We derive error estimates and present numerical results.

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