Two classes of internally $S$stable generalized RungeKutta processes which remain consistent with an inaccurate Jacobian
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 by J. D. Day and D. N. P. Murthy PDF
 Math. Comp. 39 (1982), 491509 Request permission
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.References

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Additional Information
 © Copyright 1982 American Mathematical Society
 Journal: Math. Comp. 39 (1982), 491509
 MSC: Primary 65L20
 DOI: https://doi.org/10.1090/S0025571819820669642X
 MathSciNet review: 669642