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A numerical method for KdV equation using collocation and radial basis functions

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Abstract

Recently, there has been an increasing interest in the study of initial boundary value problems for Korteweg–de Vries (KdV) equations. In this paper, we propose a numerical scheme to solve the third-order nonlinear KdV equation using collocation points and approximating the solution using multiquadric (MQ) radial basis function (RBF). The scheme works in a similar fashion as finite-difference methods. Numerical examples are given to confirm the good accuracy of the presented scheme.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran, Iran

    Mehdi Dehghan & Ali Shokri

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  1. Mehdi Dehghan
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  2. Ali Shokri
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Correspondence to Mehdi Dehghan.

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Dehghan, M., Shokri, A. A numerical method for KdV equation using collocation and radial basis functions. Nonlinear Dyn 50, 111–120 (2007). https://doi.org/10.1007/s11071-006-9146-5

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