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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