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Class 2+1 Hybrid BDF-Like methods for the numerical solutions of ordinary differential equations

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Abstract

In this article, the details of new hybrid methods have been presented to solve systems of ordinary differential equations (ODEs). These methods are based on backward differentiation formulae (BDF) where one additional stage point (or off-step point) and two step points have been used in the first derivative of the solution to improve the absolute stability regions compared with some existing methods such as BDF, extended BDF (EBDF) and modified EBDF (MEBDF). Stability domains of our new methods have been obtained showing that these methods, we say Class 2+1 Hybrid BDF-Like methods, are A-stable for order p, p=3,4, and A(α)-stable for order p, p=5, 6, 7, 8. Numerical results are also given for five test problems.

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Authors and Affiliations

  1. Department of Mathematics, University of Pune, Pune, India

    M. Ebadi

  2. Department of Mathematics, Islamic Azad University, Paprand Branch, Parand, Tehran, Iran

    M. Ebadi

  3. Department of Mathematics, M.I.T. College, Pune, India

    M. Y. Gokhale

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  1. M. Ebadi
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  2. M. Y. Gokhale
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Correspondence to M. Ebadi.

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Ebadi, M., Gokhale, M.Y. Class 2+1 Hybrid BDF-Like methods for the numerical solutions of ordinary differential equations. Calcolo 48, 273–291 (2011). https://doi.org/10.1007/s10092-011-0038-9

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  • DOI: https://doi.org/10.1007/s10092-011-0038-9

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