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IMA Journal of Numerical Analysis 2003 23(2):269-299; doi:10.1093/imanum/23.2.269
© 2003 by Institute of Mathematics and its Applications
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A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature

Dongwoo Sheen1, Ian H. Sloan2 and Vidar Thomée3

1 Department of Mathematics, Seoul National University, 151–747, Seoul, Korea 2 School of Mathematics, The University of New South Wales, 2052, Sydney, Australia 3 Department of Mathematics, Chalmers University of Technology, S-412 96, Göteborg, Sweden

We consider the discretization in time of an inhomogeneous parabolic equation in a Banach space setting, using a representation of the solution as an integral along a smooth curve in the complex left half-plane which, after transformation to a finite interval, is then evaluated to high accuracy by a quadrature rule. This reduces the problem to a finite set of elliptic equations with complex coefficients, which may be solved in parallel. The paper is a further development of earlier work by the authors, where we treated the homogeneous equation in a Hilbert space framework. Special attention is given here to the treatment of the forcing term. The method is combined with finite-element discretization in spatial variables.

Key Words: parabolic problems; parallel algorithm; Laplace transform; quadrature

Received 8 May 2002.


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