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arXiv · 1608.02089

New efficient substepping methods for exponential timestepping

Daniel Stone·Gabriel Lord
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Abstract

Exponential integrators are time stepping schemes which exactly solve the linear part of a semilinear ODE system. This class of schemes requires the approxima- tion of a matrix exponential in every step, and one successful modern method is the Krylov subspace projection method. We investigate the effect of breaking down a single timestep into arbitrary multiple substeps, recycling the Krylov subspace to minimise costs. For these recyling based schemes we analyse the lo- cal error, investigate them numerically and show they can be applied to a large system with 106 unknowns. We also propose a new second order integrator that is found using the extra information from the substeps to form a corrector to increase the overall order of the scheme. This scheme is seen to compare favourably with other order two integrators.

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Daniel Stone, Gabriel Lord. 2016-08-06. New efficient substepping methods for exponential timestepping. https://arxiv.org/abs/1608.02089

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