Runge-Kutta methods with minimum storage implementations

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43 Scopus citations


Solution of partial differential equations by the method of lines requires the integration of large numbers of ordinary differential equations (ODEs). In such computations, storage requirements are typically one of the main considerations, especially if a high order ODE solver is required. We investigate Runge-Kutta methods that require only two storage locations per ODE. Existing methods of this type require additional memory if an error estimate or the ability to restart a step is required. We present a new, more general class of methods that provide error estimates and/or the ability to restart a step while still employing the minimum possible number of memory registers. Examples of such methods are found to have good properties. © 2009 Elsevier Inc. All rights reserved.
Original languageEnglish (US)
Pages (from-to)1763-1773
Number of pages11
JournalJournal of Computational Physics
Issue number5
StatePublished - Mar 2010

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The author thanks Randy LeVeque for the suggestion to consider embedded pairs. This work was funded by a US Dept. of Energy Computational Science Graduate Fellowship.

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications


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