Two classes of internally s-stable generalized runge-kutta processes which remain consistent with an inaccurate jacobian

Day J.D. and Murthy D.N. (1982) Two classes of internally s-stable generalized runge-kutta processes which remain consistent with an inaccurate jacobian. Mathematics of Computation, 39 160: 491-509. doi:10.1090/S0025-5718-1982-0669642-X


Author Day J.D.
Murthy D.N.
Title Two classes of internally s-stable generalized runge-kutta processes which remain consistent with an inaccurate jacobian
Journal name Mathematics of Computation   Check publisher's open access policy
ISSN 0025-5718
Publication date 1982-01-01
Sub-type Article (original research)
DOI 10.1090/S0025-5718-1982-0669642-X
Volume 39
Issue 160
Start page 491
End page 509
Total pages 19
Subject 2602 Algebra and Number Theory
2605 Computational Mathematics
2604 Applied Mathematics
Abstract Generalized Runge-Kutta 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 S-stable 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 Runge-Kutta process of the same order, and second and third order processes are developed. A second class of Generalized Runge-Kutta 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.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import - Archived
 
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