Two classes of internally $S$stable generalized RungeKutta processes which remain consistent with an inaccurate Jacobian
Authors:
J. D. Day and D. N. P. Murthy
Journal:
Math. Comp. 39 (1982), 491509
MSC:
Primary 65L20
DOI:
https://doi.org/10.1090/S0025571819820669642X
MathSciNet review:
669642
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Abstract  References  Similar Articles  Additional Information
Abstract: Generalized RungeKutta Processes for stiff systems of ordinary differential equations usually require an accurate evaluation of a Jacobian at every step. However, it is possible to derive processes which are Internally Sstable when an accurate Jacobian is used but still remain consistent and highly stable if an approximate Jacobian is used. It is shown that these processes require at least as many function evaluations as an explicit RungeKutta process of the same order, and second and third order processes are developed. A second class of Generalized RungeKutta is introduced which requires that the Jacobian be evaluated accurately less than once every step. A third order process of this class is developed, and all three methods contain an error estimator similar to those of Fehlberg or England.

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Additional Information
Keywords:
Generalized RungeKutta procedure,
semiimplicit RungeKutta procedure,
approximate Jacobian,
stiff differential equations,
<I>L</I>stability,
<I>A</I>stability,
<I>S</I>stability,
Internal <I>S</I>stability
Article copyright:
© Copyright 1982
American Mathematical Society