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Numerical simulation of shallow water waves based on generalized equal width (GEW) equation by compact local integrated radial basis function method combined with adaptive residual subsampling technique

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Abstract

The shallow water equation based on the generalized equal width (GEW) equation is a PDE that can be classified in the category of hyperbolic PDEs. The current paper concerns developing an efficient and robust numerical technique to solve the shallow water equation based on the generalized equal width model. For this aim, first, the space derivative is approximated by the local collocation method via a compact integrated radial basis function. Second, the time derivative is approximated by the method of lines that yields a system of nonlinear ODEs. Furthermore, the constructed system of ODEs is solved by a fourth-order algorithm to get high-numerical results. Also, an adaptive collocation method based upon IRBF is presented for the solution of GEW. The effectiveness of our adaptive technique is shown in four examples such as interpolation, the motion of single solitary, two solitary waves and Maxwellian initial condition. It is explained in detail how the adaptive method refines the resolution.

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Acknowledgements

We thank the reviewers for their thorough review and the comments and suggestions, which significantly contributed to improving the quality of this publication

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

    Ali Ebrahimijahan, Mehdi Dehghan & Mostafa Abbaszadeh

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  1. Ali Ebrahimijahan
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  2. Mehdi Dehghan
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  3. Mostafa Abbaszadeh
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Correspondence to Mehdi Dehghan.

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Ebrahimijahan, A., Dehghan, M. & Abbaszadeh, M. Numerical simulation of shallow water waves based on generalized equal width (GEW) equation by compact local integrated radial basis function method combined with adaptive residual subsampling technique. Nonlinear Dyn 105, 3359–3391 (2021). https://doi.org/10.1007/s11071-021-06733-4

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