New efficient substepping methods for exponential timestepping
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.
Cite
@article{arxiv.1608.02089,
title = {New efficient substepping methods for exponential timestepping},
author = {Daniel Stone and Gabriel Lord},
journal= {arXiv preprint arXiv:1608.02089},
year = {2016}
}