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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, NGiven 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 SciencesVolume
463Issue
2084Pagination
1909-1924ISSN
1364-5021Department/School
School of Natural SciencesPublisher
Royal Soc LondonPlace of publication
6 Carlton House Terrace, London, England, Sw1Y 5AgRights statement
Copyright 2007 The Royal SocietyRepository Status
- Restricted