This article is cited in 3 papers

Approximation of the Jacobian matrix in $(m,2)$-methods for solving stiff problems

E. A. Novikov

Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036 Russia

Abstract: An initial value problem for stiff systems of first-order ordinary differential equations is considered. In the class of $(m,k)$-methods, two integration algorithms with a variable step size based on second $(m=k=2)$ and third $(k=2,m=3)$ order-accurate schemes are constructed in which both analytical and numerical Jacobian matrices can be frozen. A theorem on the maximum order of accuracy of $(m,2)$-methods with a certain approximation of the Jacobian matrix is proved. Numerical results are presented.

Key words: stiff problems for ordinary differential systems, $(m,k)$-methods, $L$-stability, accuracy control, freezing of Jacobian matrix.

UDC: 519.624.1

Received: 19.01.2011
Revised: 18.03.2011

 English version: Computational Mathematics and Mathematical Physics, 2011, 51:12, 2065–2078

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