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The interpolating element-free Galerkin method for solving Korteweg–de Vries–Rosenau-regularized long-wave equation with error analysis

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Abstract

The main target of this investigation is to develop a new numerical method for solving a class of wave models, i.e., the Korteweg–de Vries–Rosenau-regularized long-wave equation with application in plasma physics. The developed technique is concerning the interpolating element-free Galerkin method. The test and trial functions for the interpolating element-free Galerkin technique have been chosen from the interpolating moving least squares approximation. The interpolating moving least squares approximation shape functions unlike the moving least squares shape functions have the delta Kronecker property due to the use of a singular weight function. The stability and convergence of the new scheme are analyzed. Furthermore, the existence and uniqueness of solution have been proved for the full-discrete scheme. Finally, several examples in one- and two-dimensional cases have been studied to confirm the influence of the new scheme.

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Acknowledgements

We would like to give our sincere gratitude to the reviewers for their comments and suggestions that greatly improved the manuscript.

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  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, 15914, Iran

    Mostafa Abbaszadeh & Mehdi Dehghan

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  1. Mostafa Abbaszadeh
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Most of the natural phenomena can be simulated by the partial differential equations (PDEs). In the meantime, the nonlinear PDEs have important roles. In other words, many phenomena in nature and industry have been modeled by PDEs. There are several numerical and analytical procedures to solve PDEs such as finite difference, finite element, finite volume and meshless methods in which each of them has its own advantages and disadvantages. Nevertheless, for solving some PDEs, we have to use a special method.

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Abbaszadeh, M., Dehghan, M. The interpolating element-free Galerkin method for solving Korteweg–de Vries–Rosenau-regularized long-wave equation with error analysis. Nonlinear Dyn 96, 1345–1365 (2019). https://doi.org/10.1007/s11071-019-04858-1

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