A Numerical Meshfree Technique for the Solution of the MEW Equation
Sirajul Haq; Siraj-ul-Islam; and Arshed Ali

doi:10.3970/cmes.2008.038.001
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 38, No. 1, pp. 1-24, 2008
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Keywords Generalized equal width wave (GEW) equation, Modified equal width wave (MEW) equation, Radial basis functions (RBFs), Solitary wave, Stability analysis.
Abstract In this paper we propose a meshfree technique for the numerical solution of the modified equal width wave (MEW) equation. Combination of collocation method using the radial basis functions (RBFs) with first order accurate forward difference approximation is employed for obtaining meshfree solution of the problem. Different types of RBFs are used for this purpose. Performance of the proposed method is successfully tested in terms of various error norms. In the case of non-availability of exact solution, performance of the new method is compared with the results obtained from the existing methods. Propagation of a solitary wave, interaction of two solitary waves, a train of solitary waves, conservative properties in terms of mass, momentum and energy are investigated. The elementary stability analysis of the method is discussed both theoretically and numerically.
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