NUMERICAL METHODS FOR MULTIDIMENSIONAL INTEGRAL EQUATIONS.

Ivan G. Graham

NUMERICAL METHODS FOR MULTIDIMENSIONAL INTEGRAL EQUATIONS.

Department of Mathematical Sciences

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Abstract

The numerical solution of multidimensional Fredholm integral equations of the second kind are considered, using the Galerkin and collocation methods and their iterative variants. The authors prove convergence, and examine superconvergence phenomena for the iterated solution. In particular O(h**2) convergence is proved for methods based on simple piecewise constant functions. Numerical results are presented for the two dimensional singular equation arising from the skin effect current distribution problem. Iterative refinement methods are used to minimise the computational cost of the numerical scheme.

Original language	English
Title of host publication	Constructive Methods for the Practical Treatment of Integral Equations
Editors	John Noye, Clive Fletcher
Publisher	North-Holland Publishing Co.
Pages	335-351
Number of pages	17
ISBN (Print)	0444875271
Publication status	Published - 1984

ASJC Scopus subject areas

General Engineering

Cite this

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title = "NUMERICAL METHODS FOR MULTIDIMENSIONAL INTEGRAL EQUATIONS.",

abstract = "The numerical solution of multidimensional Fredholm integral equations of the second kind are considered, using the Galerkin and collocation methods and their iterative variants. The authors prove convergence, and examine superconvergence phenomena for the iterated solution. In particular O(h**2) convergence is proved for methods based on simple piecewise constant functions. Numerical results are presented for the two dimensional singular equation arising from the skin effect current distribution problem. Iterative refinement methods are used to minimise the computational cost of the numerical scheme.",

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N2 - The numerical solution of multidimensional Fredholm integral equations of the second kind are considered, using the Galerkin and collocation methods and their iterative variants. The authors prove convergence, and examine superconvergence phenomena for the iterated solution. In particular O(h**2) convergence is proved for methods based on simple piecewise constant functions. Numerical results are presented for the two dimensional singular equation arising from the skin effect current distribution problem. Iterative refinement methods are used to minimise the computational cost of the numerical scheme.

AB - The numerical solution of multidimensional Fredholm integral equations of the second kind are considered, using the Galerkin and collocation methods and their iterative variants. The authors prove convergence, and examine superconvergence phenomena for the iterated solution. In particular O(h**2) convergence is proved for methods based on simple piecewise constant functions. Numerical results are presented for the two dimensional singular equation arising from the skin effect current distribution problem. Iterative refinement methods are used to minimise the computational cost of the numerical scheme.

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M3 - Chapter in a published conference proceeding

AN - SCOPUS:0021700443

SN - 0444875271

SP - 335

EP - 351

BT - Constructive Methods for the Practical Treatment of Integral Equations

A2 - Noye, John

A2 - Fletcher, Clive

PB - North-Holland Publishing Co.

ER -

NUMERICAL METHODS FOR MULTIDIMENSIONAL INTEGRAL EQUATIONS.

Abstract

ASJC Scopus subject areas

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