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A class of A(α)-stable numerical methods for stiff problems in ordinary differential equations

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Abstract

The A(α)-stable numerical methods (ANMs) for the number of steps k ≤ 7 for stiff initial value problems (IVPs) in ordinary differential equations (ODEs) are proposed. The discrete schemes proposed from their equivalent continuous schemes are obtained. The scaled time variable t in a continuous method, which determines the discrete coefficients of the discrete method, is chosen in such a way as to ensure that the discrete scheme attains a high order and A(α)-stability. We select the value of α for which the schemes proposed are absolutely stable. The new algorithms are found to have a comparable accuracy with that of the backward differentiation formula (BDF) discussed in [12] which implements the Ode15s in the Matlab suite.

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Authors and Affiliations

  1. Department ofMathematics, University of Benin, P.M.B 1154, Benin City, Edo State, Nigeria

    R. I. Okuonghae

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  1. R. I. Okuonghae
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Correspondence to R. I. Okuonghae.

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Original Russian Text © R.I. Okuonghae, 2013, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2013, Vol. 16, No. 4, pp. 347–364.

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Okuonghae, R.I. A class of A(α)-stable numerical methods for stiff problems in ordinary differential equations. Numer. Analys. Appl. 6, 298–313 (2013). https://doi.org/10.1134/S1995423913040058

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  • DOI: https://doi.org/10.1134/S1995423913040058

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