Runge-Kutta methods with minimum storage implementations

Ketcheson, David I.

Runge-Kutta methods with minimum storage implementations

Type

Article

Authors

Ketcheson, David I.

KAUST Department

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Numerical Mathematics Group

Date

2010-03

Abstract

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.

Citation

Ketcheson, D. I. (2010). Runge–Kutta methods with minimum storage implementations. Journal of Computational Physics, 229(5), 1763–1773. doi:10.1016/j.jcp.2009.11.006

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.