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A meshless method for solving mKdV equation. (English) Zbl 1282.65123
Summary: A meshless method based on a global collocation with radial basis functions for the numerical solution of the modified Korteweg-de Vries (mKdV) equation is presented. Standard types of radial basis functions are applied in the method of collocation. The stability analysis of the method is dealt with using a linearized stability analysis. The method’s accuracy and efficiency are examined by the simulation of a single soliton and interaction of two solitary waves. The four invariants of the motion are evaluated to determine the conservation properties of the method. A comparison with some earlier reported results is also carried out.

65M70Spectral, collocation and related methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
Full Text: DOI
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