RBFs approximation method for Kawahara equation
In this paper, we apply radial basis function (RBF) method for the numerical solution of Kawahara equation. Derivatives of interpolation are used to approximate the spatial derivatives and the temporal derivative approximated by a low order forward difference scheme. Computational experiments are performed for single soliton, two solitons, and three solitons interaction to examine accuracy of the method. The results obtained by the present method are in good agreement with exact solutions and some earlier work in literature. Accuracy of the method is estimated in terms of the error norms L2, L? L ? , the three invariants, number of nodes in the domain of influence, time step size, parameter dependent, and parameter independent RBFs.
rbfs kawahara equation single soliton solitons interaction meshfree approximation method