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A direct variable step block multistep method for solving general third-order ODEs

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Abstract

This paper discusses a direct three-point implicit block multistep method for direct solution of the general third-order initial value problems of ordinary differential equations using variable step size. The method is based on a pair of explicit and implicit of Adams type formulas which are implemented in PE(CE)t mode and in order to avoid calculating divided difference and integration coefficients all the coefficients are stored in the code. The method approximates the numerical solution at three equally spaced points simultaneously. The Gauss Seidel approach is used for the implementation of the proposed method. The local truncation error of the proposed scheme is studied. Numerical examples are given to illustrate the efficiency of the method.

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  1. Department of Mathematics, Faculty of Science, UPM, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia

    Siamak Mehrkanoon

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  1. Siamak Mehrkanoon
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Correspondence to Siamak Mehrkanoon.

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Mehrkanoon, S. A direct variable step block multistep method for solving general third-order ODEs. Numer Algor 57, 53–66 (2011). https://doi.org/10.1007/s11075-010-9413-x

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  • DOI: https://doi.org/10.1007/s11075-010-9413-x

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