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The numerical solution of some elliptic boundary value problems by integral operator methods

Part of the Lecture Notes in Mathematics book series (LNM,volume 430)

Abstract

An integral representation for the solution of elliptic equations of the form Δnu - P(r2)u=0, developed by Gilbert, is used to construct approximate solutions for problems of this type. Properties of the G-function, needed in the integral representation, are discussed and a numerical scheme for its computation is given. The approximate G-function is used to represent the solution and minimization techniques are used to satisfy the boundary conditions. A discussion of the practical usefulness of methods of this type is given.

This research was supported in part by the Air Force Office of Scientific Research through grant AFOSR-71-2205.

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© 1974 Springer-Verlag

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Gilbert, R.P., Linz, P. (1974). The numerical solution of some elliptic boundary value problems by integral operator methods. In: Colton, D.L., Gilbert, R.P. (eds) Constructive and Computational Methods for Differential and Integral Equations. Lecture Notes in Mathematics, vol 430. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066271

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  • DOI: https://doi.org/10.1007/BFb0066271

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07021-4

  • Online ISBN: 978-3-540-37302-5

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