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Boundary tracing and boundary value problems: II. Applications

journal contribution
posted on 2023-05-18, 17:34 authored by Anderson, ML, Andrew BassomAndrew Bassom, Fowkes, N
This is the second of a pair of papers describing the use of boundary tracing for boundary value problems. In the preceding article, the theory of the technique was explained and it was shown how it enables one to use known exact solutions of partial differential equations to generate new solutions. Here, we illustrate the use of the technique by applying it to three equations of practical significance: Helmholtz’s equation, Poisson’s equation and the nonlinear constant mean curvature equation. A variety of new solutions are obtained and the potential of the technique for further application outlined.

History

Publication title

Proceedings of the Royal Society A

Volume

463

Issue

2084

Pagination

1925-1938

ISSN

1364-5021

Department/School

School of Natural Sciences

Publisher

Royal Soc London

Place of publication

6 Carlton House Terrace, London, England, Sw1Y 5Ag

Rights statement

Copyright 2007 The Royal Society

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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