On the implementation of exponential methods for semilinear parabolic equations

Details On the implementation of exponential methods for semilinear parabolic equations On the implementation of exponential methods for semilinear parabolic equations

2008-10-22

arxiv.org/abs/0810.4101v1

Mathematics

Numerical Analysis

17 pages, 7 figures

Scientific paper

The time integration of semilinear parabolic problems by exponential methods of different kinds is considered. A new algorithm for the implementation of these methods is proposed. The algorithm evaluates the operators required by the exponential methods by means of a quadrature formula that converges like $O(e^{-cK/\ln K})$, with $K$ the number of quadrature nodes. The algorithm allows also the evaluation of the associated scalar mappings and in this case the quadrature converges like $O(e^{-cK})$. The technique is based on the numerical inversion of sectorial Laplace transforms. Several numerical illustrations are provided to test the algorithm.

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