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The Computer Journal 1978 21(4):363-365; doi:10.1093/comjnl/21.4.363
© 1978 by British Computer Society
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On the computational aspects of semi-implicit Runge-Kutta methods

J. R. Cash1 and C. B. Liem2 *

1 Department of Mathematics, Imperial College of Science and Technology, Queen's Gate London, UK, 2 Department of Mathematics, Hong Kong Polytechnic, Hong Kong

In recent years the problem of obtaining an approximate numerical solution of stiff systems of first order ordinary differential equations has received a great deal of attention. One important class of numerical procedures suitable for tackling this problem is the class of semi-implicit Runge-Kutta procedures originally proposed by Rosenbrock. Although a great many algorithms belonging to this particular class have now been proposed a detailed comparison between them on a truly representative class of stiff system has not so far been made. Moreover an analysis of the computational aspects of semi-implicit Runge-Kutta schemes is noticeable only by its absence. The purpose of the present paper is to examine some of these computational aspects in the third order case in some detail with the aim of making some specific recommendations regarding which methods should be used in practice. The details of some fairly exhaustive numerical experiments are also presented.

Received May 1977.

* Now at Department of Mathematics, Hong Kong, Polytechnic

§ Department of Mathematics, Imperial College of Science and Technology, Queen's Gate London SW7 2BZ


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