# Computing semigroups with error control

@article{Colbrook2021ComputingSW, title={Computing semigroups with error control}, author={Matthew J. Colbrook}, journal={ArXiv}, year={2021}, volume={abs/2110.06350} }

We develop an algorithm that computes strongly continuous semigroups on infinitedimensional Hilbert spaces with explicit error control. Given a generator A, a time t > 0, an arbitrary initial vector u0 and an error tolerance > 0, the algorithm computes exp(tA)u0 with error bounded by . The algorithm is based on a combination of a regularized functional calculus, suitable contour quadrature rules, and the adaptive computation of resolvents in infinite dimensions. As a particular case, we show…

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