New efficient substepping methods for exponential timestepping

G.J. Lord and D. Stone

Applied Mathematics and Computation, 2017, vol. 307, issue C, 342-365

Abstract: Exponential integrators are time stepping schemes which exactly solve the linear part of a semilinear ODE system. This class of schemes requires the approximation 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 recycling based schemes we analyse the local 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 favorably with other order two integrators.

Keywords: Exponential integrators; Krylov subspace methods; Advection-diffusion-reaction equations (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300317301637
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:307:y:2017:i:c:p:342-365

DOI: 10.1016/j.amc.2017.02.052

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().