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A computational study of solitary wave solutions of Kawahara-type equations by meshless spectral interpolation method

Manzoor Hussain

Department of Mathematics & Statistics, Bacha Khan University, Charsadda, KP, Pakistan

Faculty of Engineering Sciences, GIK Institute, Topi-23640, KP, Pakistan

E-mail Address: manzoor366@gmail.com

Corresponding author.

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and

Sirajul Haq

Faculty of Engineering Sciences, GIK Institute, Topi-23640, KP, Pakistan

E-mail Address: siraj_jcs@yahoo.co.in

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https://doi.org/10.1142/S012918311950102XCited by:4 (Source: Crossref)

Abstract

In this paper, a meshless spectral radial point interpolation (MSRPI) method using weighted $θ$ $θ$ -scheme is formulated for the numerical solutions of a class of nonlinear Kawahara-type evolutionary equations. The formulated method is applied for simulation of single and double solitary waves motion, wave generation and oscillatory shock waves propagation. Quality of approximation is measured via discrete $L_{\infty}$ $L_{\infty}$ , $L_{2}$ $L_{2}$ and $L_{rms}$ $L_{rms}$ error norms. Three invariant quantities corresponding to mass, momentum and energy are also computed for the method validation. Stability analysis of the proposed method is briefly discussed and verified computationally. Comparison of the obtained results are made with other existing results in the literature revealing the method superiority.

Keywords:

PACS: 02.60.Cb, 02.70.Jn, 47.11.Fg, 47.35.Fg

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