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Numerical Solutions of the KdV Equation Using B-Spline Functions

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Abstract

A numerical technique based on the finite difference and collocation methods is presented for the solution of Korteweg–de Vries (KdV) equation. The integration relations between any two families of B-spline functions are presented and are utilized to reduce the solution of KdV equation to the solution of linear algebraic equations. Numerical simulations for three test examples have been demonstrated to validate the technique proposed in the current paper. It is found that the simulating results are in good agreement with the exact solutions.

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Acknowledgements

The research on which this paper is based was supported by the research fund of the University of Tabriz.

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  1. Department of Applied Mathematics, University of Tabriz, Tabriz, Iran

    Mehrdad Lakestani

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  1. Mehrdad Lakestani
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Correspondence to Mehrdad Lakestani.

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Lakestani, M. Numerical Solutions of the KdV Equation Using B-Spline Functions. Iran J Sci Technol Trans Sci 41, 409–417 (2017). https://doi.org/10.1007/s40995-017-0260-7

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  • DOI: https://doi.org/10.1007/s40995-017-0260-7

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