10.1007/s40096-021-00375-8

The impact of LRBF-FD on the solutions of the nonlinear regularized long wave equation

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  • M. N. Rasoulizadeh*1,
  • O. Nikan2,
  • Z. Avazzadeh3,
  1. Department of Mathematics, Velayat University, Iranshahr, IR
  2. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, IR
  3. Department of Applied Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou, 215123, CN

Published in Issue 2021-01-31

How to Cite

Rasoulizadeh, M. N., Nikan, O., & Avazzadeh, Z. (2021). The impact of LRBF-FD on the solutions of the nonlinear regularized long wave equation. Mathematical Sciences, 15(4 (December 2021). https://doi.org/10.1007/s40096-021-00375-8
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Abstract

Abstract This paper develops a method for the numerical solution of the nonlinear regularized long wave equation. This method discretizes the unknown solution in two main schemes. The time discretization is accomplished by means of an implicit method based on the θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document} -weighted and finite difference methods, while the spatial discretization is described with the help of the finite difference scheme derived from the local radial basis function method. The advantage of the local collocation method is based only the discretization nodes located in each sub-domain, requiring to be considered when obtaining the approximate solution at every node. It also tackles the ill-conditioning problem derived from global collocation method. Besides, the stability analysis of the proposed method is analyzed and the accuracy of it is examined with L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\infty }$$\end{document} and L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document} norm errors. At the end, the results obtained by the proposed method are compared with the methods given in previous works and it indicates an improvement in comparison with previous works.

Keywords

  • Nonlinear regularized long wave,
  • Radial basis function,
  • LRBF-FD,
  • Stability analysis,
  • RLW equation

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