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Numerical solution of the regularized long wave equation using nonpolynomial splines

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Abstract

In this paper, we employ nonpolynomial spline (NPS) basis functions to obtain approximate solutions of the regularized long wave (RLW) equation. By considering suitable relevant parameters, it is shown that the local truncation error behaves O(k 2+h 2) with respect to the time and space discretization. Numerical stability of the method is investigated by using a linearized stability analysis. To illustrate the applicability and efficiency of the aforementioned basis, we compare obtained numerical results with other existing recent methods. Motion of single solitary wave and double and triple solitary waves, wave undulation, generation of solitary waves using the Maxwellian initial condition and conservation properties of mass, energy, and momentum of numerical solutions of the equation are dealt with.

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Authors and Affiliations

  1. Department of Mathematics, Tafresh University, Tafresh, 39518-79611, Iran

    N. G. Chegini, A. Salaripanah & D. Isvand

  2. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    R. Mokhtari

Authors
  1. N. G. Chegini
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  2. A. Salaripanah
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  3. R. Mokhtari
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  4. D. Isvand
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Correspondence to R. Mokhtari.

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Chegini, N.G., Salaripanah, A., Mokhtari, R. et al. Numerical solution of the regularized long wave equation using nonpolynomial splines. Nonlinear Dyn 69, 459–471 (2012). https://doi.org/10.1007/s11071-011-0277-y

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  • DOI: https://doi.org/10.1007/s11071-011-0277-y

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