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

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## Abstract

An integral representation for the solution of elliptic equations of the form Δ_{n}u - P(r^{2})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.

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