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Boundary tracing and boundary value problems: I. Theory


Anderson, ML and Bassom, AP and Fowkes, N, Boundary tracing and boundary value problems: I. Theory, Proceedings of the Royal Society A. Mathematical, Physical and Engineering Sciences, 463, (2084) pp. 1909-1924. ISSN 1364-5021 (2007) [Refereed Article]

Copyright Statement

Copyright 2007 The Royal Society

DOI: doi:10.1098/rspa.2007.1858


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.

Item Details

Item Type:Refereed Article
Keywords:boundary tracing; partial differential equations; exact solutions
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:107106
Year Published:2007
Web of Science® Times Cited:2
Deposited By:Mathematics and Physics
Deposited On:2016-03-04
Last Modified:2016-07-06

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