A high order parallel method for time discretization of parabolic type equations based on Laplace transformation and quadrature
Vidar Thomée 11 Department of Mathematics, Chalmers University of Technology, S-412 96 Göteborg, Sweden
Received by the editors June 14, 2004
We consider the discretization in time of a parabolic equation, using a representation of the solution as an integral along a smooth curve in the complex left half plane. The integral is then evaluated to high accuracy by a quadrature rule. This reduces the problem to a finite set of elliptic equations, which may be solved in parallel. The procedure is combined with finite element discretization in the spatial variables. The method is also applied to some parabolic type evolution equations with memory.
AMS subject classifications: 65N30, 65N15
Key words: parabolic type; Laplace; parallel method and high order quadrature