Vol. 1, No. 1, 2006

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
On the spectral deferred correction of splitting methods for initial value problems

Thomas Hagstrom and Ruhai Zhou

Vol. 1 (2006), No. 1, 169–205
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.

Keywords
splitting methods, deferred correction, stability regions
Mathematical Subject Classification 2000
Primary: 65L06, 65M20
Milestones
Received: 23 August 2005
Accepted: 30 September 2006
Published: 14 May 2007
Authors
Thomas Hagstrom
Department of Mathematics and Statistics
The University of New Mexico
Albuquerque, NM 87131
United States
Ruhai Zhou
Department of Mathematics and Statistics
Old Dominion University
Norfolk, VA 23529
United States