Partitioning strategies in Runge-Kutta type methods

The numerical solution of ode's suffers from stability constraints, if there are solution components with different time constants. Two recommended approaches in software packages to handle these difficulties (i) automatic switching between stiff and nonstiff methods and (ii) the use of partiti...

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Bibliographic Details
Published in:IMA journal of numerical analysis 1993-04, Vol.13 (2), p.303-319
Main Authors: WEINER, R., ARNOLD, M., RENTROP, P., STREHMEL, K.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sciences and techniques of general use
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Summary:The numerical solution of ode's suffers from stability constraints, if there are solution components with different time constants. Two recommended approaches in software packages to handle these difficulties (i) automatic switching between stiff and nonstiff methods and (ii) the use of partitioned methods for a given splitting into stiff and nonstiff subsystems, are presented and investigated for Runge-Kutta type methods. A strategy for a dynamic partitioning in these methods is discussed. Numerical results illustrate the efficiency of partitioning.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/13.2.303