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We treat the time discretization of an initial-value problem for a homogeneous abstract parabolic equation by rst using a representation of the solution as an integral along the boundary of a sector in the right half of the complex plane, then transforming this into a real integral on the nite interval (0; 1), and nally applying a standard quadrature formula to this integral. The method requires the solution of a nite set of elliptic problems with complex coecients, which are independent and may therefore be done in parallel. The method is combined with spatial discretization by nite elements.

A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature