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Numerical solution of an evolution equation with a positive-type memory term

Published online by Cambridge University Press:  17 February 2009

W. McLean
Affiliation:
School of Mathematics, University of New South Wales, Sydney 2033
V. Thomée
Affiliation:
Department of Mathematics, Chalmers University of Technology, S-412 96 Göteborg, Sweden
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Abstract

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We study the numerical solution of an initial-boundary value problem for a Volterra type integro-differential equation, in which the integral operator is a convolution product of a positive-definite kernel and an elliptic partial-differential operator. The equation is discretised in space by the Galerkin finite-element method and in time by finite differences in combination with various quadrature rules which preserve the positive character of the memory term. Special attention is paid to the case of a weakly singular kernel. Error estimates are derived and numerical experiments reported.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1993

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