# A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature

@article{Sheen2003APM, title={A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature}, author={Dongwoo Sheen and Ian H. Sloan and Vidar Thom{\'e}e}, journal={Ima Journal of Numerical Analysis}, year={2003}, volume={23}, pages={269-299} }

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…

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