Time discretization via Laplace transformation of an integro-differential equation of parabolic type
Artikel i vetenskaplig tidskrift, 2006

We consider the discretization in time of an inhomogeneous parabolic integro-differential equation, with a memory term of convolution type, in a Banach space setting. The method is based on representing the solution as an integral along a smooth curve in the complex plane which is evaluated to high accuracy by quadrature, using the approach in recent work of López-Fernández and Palencia. This reduces the problem to a finite set of elliptic equations with complex coefficients, which may be solved in parallel. The method is combined with finite element discretization in the spatial variables to yield a fully discrete method. The paper is a further development of earlier work by the authors, which on the one hand treated purely parabolic equations and, on the other, an evolution equation with a positive type memory term.


William McLean

University of New South Wales (UNSW)

Ian Sloan

University of New South Wales (UNSW)

Vidar Thomee

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Numerische Mathematik

0029-599X (ISSN) 0945-3245 (eISSN)

Vol. 102 497-522