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Boundary tracing and boundary value problems: I. Theory

journal contribution
posted on 2023-05-18, 17:33 authored by Anderson, ML, Andrew BassomAndrew Bassom, Fowkes, N
Given an exact solution of a partial differential equation in two dimensions, which satisfies suitable conditions on the boundary of the domain of interest, it is possible to deform the boundary curve so that the conditions remain fulfilled. The curves obtained in this manner can be patched together in various ways to generate a remarkably broad range of domains for which the boundary constraints remain satisfied by the initial solution. This process is referred to as boundary tracing and works for both linear and nonlinear problems. This article presents a general theoretical framework for implementing the technique for two-dimensional, second-order, partial differential equations with a general flux condition imposed around the boundary. A couple of simple examples are presented that serve to demonstrate the analytical tools in action. Applications of more intrinsic interest are discussed in the following paper.

History

Publication title

Proceedings of the Royal Society A. Mathematical, Physical and Engineering Sciences

Volume

463

Issue

2084

Pagination

1909-1924

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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