Geodesic
Approximation of the Jacobian matrix in $(m,2)$-methods for solving stiff problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 12, pp. 2194-2208 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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E. A. Novikov. Approximation of the Jacobian matrix in $(m,2)$-methods for solving stiff problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 12, pp. 2194-2208. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_12_a5/

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