A meshless method for solving mKdV equation

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 methodʼs 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.