A mesh-free method for the numerical solution of the KdV–Burgers equation

This paper formulates a simple classical radial basis functions (RBFs) collocation (Kansa) method for the numerical solution of the nonlinear dispersive and dissipative KdV–Burgers’ (KdVB) equation. The computed results show implementation of the method to nonlinear partial differential equations. This method has an edge over traditional methods such as finite-difference and finite element methods because it does not require a mesh to discretize the problem domain, and a set of scattered nodes in the domain of influence provided by initial data is required for the realization of the method. Accuracy of the method is assessed in terms of error norms L2,L∞L2,L∞, number of nodes in the domain of influence, parameter dependent RBFs and time step length. Numerical experiments demonstrate accuracy and robustness of the method for solving nonlinear dispersive and dissipative problems.