Numerical solution of complex modified Korteweg–de Vries equation by mesh-free collocation method

Abstract

A mesh-free method based on radial basis functions (RBFs) is proposed for the solution of complex modified Korteweg–de Vries (CMKdV) equation. The mesh-free algorithm is based on scattered data interpolation along with approximating functions known as radial basis functions (RBFs). A set of scattered nodes provided by initial data is used for solution of the problem. Computational experiments examine the accuracy of the method in terms of error norms L2, L∞ and the three invariants I1, I2 and I3. The results obtained by the method are in good agreement with exact solutions and the earlier work.