Communications in Applied Mathematics and Computational Science

On the spectral deferred correction of splitting methods for initial value problems

Thomas Hagstrom and Ruhai Zhou

Full-text: Open access

Abstract

Spectral deferred correction is a flexible technique for constructing high-order, stiffly-stable time integrators using a low order method as a base scheme. Here we examine their use in conjunction with splitting methods to solve initial-boundary value problems for partial differential equations. We exploit their close connection with implicit Runge–Kutta methods to prove that up to the full accuracy of the underlying quadrature rule is attainable. We also examine experimentally the stability properties of the methods for various splittings of advection-diffusion and reaction-diffusion equations.

Article information

Source
Commun. Appl. Math. Comput. Sci., Volume 1, Number 1 (2006), 169-205.

Dates
Received: 23 August 2005
Accepted: 30 September 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.camcos/1513798509

Digital Object Identifier
doi:10.2140/camcos.2006.1.169

Mathematical Reviews number (MathSciNet)
MR2299441

Zentralblatt MATH identifier
1105.65076

Subjects
Primary: 65L06: Multistep, Runge-Kutta and extrapolation methods 65M20: Method of lines

Keywords
splitting methods deferred correction stability regions

Citation

Hagstrom, Thomas; Zhou, Ruhai. On the spectral deferred correction of splitting methods for initial value problems. Commun. Appl. Math. Comput. Sci. 1 (2006), no. 1, 169--205. doi:10.2140/camcos.2006.1.169. https://projecteuclid.org/euclid.camcos/1513798509


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