Manchester Applied Mathematics and Numerical Analysis Seminars

Spring 1999

February 24, 1999, 2.30 pm

Lecture Theatre OF/B9 Oddfellows Hall (Material Science)

Solving parabolic problems without time stepping

Prof. Ian H. Sloan, School of Mathematics, University of New South Wales

In this joint work with Vidar Thomee (Chalmers) and Dongwoo Sheen (Seoul), we consider a different approach to certain parabolic problems: instead of carrying the solution forward through small time increments, we make use of a contour integral representation of the Laplace transform of the solution. After a suitable contour deformation, the solution is approximated by a suitable quadrature formula. To each quadrature point there corresponds a (complex-valued) elliptic problem, which can be solved in a standard way.

The approach is inherently parallelisable (in contrast to step-by-step methods), because the finite set of elliptic problems can be solved in any order. The method seems to be of practical interest for appropriate problems.

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