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On the numerical solution of a class of partial differential equations

Published online by Cambridge University Press:  24 October 2008

A. S. Douglas
A. S. Douglas
Affiliation:
Mathematical Laboratory, Cambridge
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Abstract

For a suitable choice of E*, the solution as t becomes large of the equation

where Y is given independent of t over the space boundaries, tends to the ground state solution of the wave equation

with the same boundary conditions on P as on Y. As a preliminary to using this relation to solve wave equations in more than one variable, the solution of the equation

has been studied. Methods of numerical solution are discussed, and the convergence of these is examined. Some practical experiments using an electronic computing machine are described.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 2 , April 1958 , pp. 214 - 218
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

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