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Solving nonlinear parabolic PDEs via extended hybrid BDF methods

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Abstract

The details of new methods based on backward differentiation formulas (BDF) for the MOL solution of one-dimensional nonlinear time dependent PDEs are presented. In these extended hybrid BDF methods, we say EHBDF, one additional stage point (or off-step point) together with one step point have been used in the first derivative of the solution. All presented methods, of order p, p = 2,3,..., 12, are A(α)-stable whereas they have wide stability regions comparing with those of some known methods such as BDF, extended BDF (EBDF) and modified EBDF (MEBDF) methods.

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Authors and Affiliations

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

    Moosa Ebadi

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

    M. Y. Gokhale

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

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Ebadi, M., Gokhale, M.Y. Solving nonlinear parabolic PDEs via extended hybrid BDF methods. Indian J Pure Appl Math 45, 395–412 (2014). https://doi.org/10.1007/s13226-014-0070-y

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  • DOI: https://doi.org/10.1007/s13226-014-0070-y

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