Asymptotic behaviour of numerical solutions of an evolution equation with memory

Article type: Research Article

Authors: McLean, W.^; | Thomée, V.

Affiliations: School of Mathematics, The University of New South Wales, Sydney 2052, Australia, E-mail: [email protected] | Department of Mathematics, Chalmers University of Technology, S-412 96 Göteborg, Sweden, E-mail: [email protected]

Note: [] Both authors were supported by the Australian Research Council.

Abstract: We study the exponential decay of discrete and continuous solutions of a Volterra type integro-differential equation, in which the integral operator is a convolution of an exponentially decreasing scalar positive definite kernel and a positive definite operator, such as an elliptic differential operator. The equation is discretized in time by the backward Euler method in combination with convolution quadrature.

Keywords: Partial integro-differential equation, convolution quadrature

DOI: 10.3233/ASY-1997-14303

Journal: Asymptotic Analysis, vol. 14, no. 3, pp. 257-276, 1997