Solitary wave solutions of the MRLW equation using radial basis functions

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Abstract

In this study, traveling wave solutions of the modified regularized long wave (MRLW) equation are simulated by using the meshless method based on collocation with well-known radial basis functions. The method is tested for three test problems which are single solitary wave motion, interaction of two solitary waves and interaction of three solitary waves. Invariant values for all test problems are calculated, also L2, L norms and values of the absolute error for single solitary wave motion are calculated. Numerical results by using the meshless method with different radial basis functions are presented. Figures of wave motions for all test problems are shown. Altogether, meshless methods with radial basis functions solve the MRLW equation very satisfactorily.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 235–247, 2012

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