Vol. 10, No. 1, 2015

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Revisionist integral deferred correction with adaptive step-size control

Andrew J. Christlieb, Colin B. Macdonald, Benjamin W. Ong and Raymond J. Spiteri

Vol. 10 (2015), No. 1, 1–25
Abstract

Adaptive step-size control is a critical feature for the robust and efficient numerical solution of initial-value problems in ordinary differential equations. In this paper, we show that adaptive step-size control can be incorporated within a family of parallel time integrators known as revisionist integral deferred correction (RIDC) methods. The RIDC framework allows for various strategies to implement step-size control, and we report results from exploring a few of them.

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Keywords
initial-value problems, revisionist integral deferred correction, parallel time integrators, local error estimation, adaptive step-size control
Mathematical Subject Classification 2010
Primary: 65H10, 65L05, 65Y05
Milestones
Received: 9 October 2013
Revised: 10 December 2014
Accepted: 17 December 2014
Published: 27 March 2015
Authors
Andrew J. Christlieb
Department of Mathematics
Michigan State University
East Lansing, 48823
United States
Colin B. Macdonald
Mathematical Institute
Oxford University
Oxford
OX2 6GG
United Kingdom
Benjamin W. Ong
Department of Mathematics
Michigan Technological University
Houghton, MI 49931
United States
Raymond J. Spiteri
Department of Computer Science
University of Saskatchewan
Saskatoon S7N 5C9
Canada