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Explicit multistep method for the numerical solution of stiff differential equations

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Abstract

An explicit multistep method of variable order for integrating stiff systems with high accuracy and low computational costs is examined. To stabilize the computational scheme, componentwise estimates are used for the eigenvalues of the Jacobian matrix having the greatest moduli. These estimates are obtained at preliminary stages of the integration step. Examples are given to demonstrate that, for certain stiff problems, the method proposed is as efficient as the best implicit methods.

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Authors and Affiliations

  1. Bauman State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 107005, Russia

    L. M. Skvortsov

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  1. L. M. Skvortsov
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Original Russian Text © L.M. Skvortsov, 2007, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2007, Vol. 47, No. 6, pp. 959–967.

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Skvortsov, L.M. Explicit multistep method for the numerical solution of stiff differential equations. Comput. Math. and Math. Phys. 47, 915–923 (2007). https://doi.org/10.1134/S0965542507060036

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  • DOI: https://doi.org/10.1134/S0965542507060036

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