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A Generalized Family of Symmetric Multistep Methods with Minimal Phase-Lag for Initial Value Problems in Ordinary Differential Equations

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Abstract

In the present paper, we formulate a generalized family of symmetric multistep methods (GFSMMs) for solving initial value problems in ordinary differential equations. Future solution values are inherent in the GFSMMs. However, a purely interpolatory approach is applied for the derivation of the GFSMMs and a detailed theoretical and computational study is presented. These include the order, stability, interval of periodicity, and phase-lag (PL) analysis of the methods. Some of the proposed methods herein possess minimal PL error constants, while some have high-order PL. Also, some of the proposed GFSMMs are P-stable, while some exhibit multiple intervals of periodicity. The application of the newly formulated schemes are demonstrated in the numerical experiments presented.

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Acknowledgements

This research work has greatly benefited from the Advanced Research Laboratory, Department of Mathematics, University of Benin, of Prof. Francis O. Otunta. This is to express our gratitude to the anonymous reviewer whose comments have greatly improved the quality of this paper.

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Authors and Affiliations

  1. African Institute for Mathematical Sciences, Kigali, Rwanda

    Oluwasegun M. Ibrahim

  2. Advanced Research Laboratory, Department of Mathematics, University of Benin, Benin, Nigeria

    Oluwasegun M. Ibrahim & Monday N. O. Ikhile

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  1. Oluwasegun M. Ibrahim
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  2. Monday N. O. Ikhile
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Correspondence to Oluwasegun M. Ibrahim.

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Ibrahim, O.M., Ikhile, M.N.O. A Generalized Family of Symmetric Multistep Methods with Minimal Phase-Lag for Initial Value Problems in Ordinary Differential Equations. Mediterr. J. Math. 17, 87 (2020). https://doi.org/10.1007/s00009-020-01507-5

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