COLLOCATION METHODS BASED ON RADIAL BASIS FUNCTIONS FOR THE COUPLED KLEIN-GORDON-SCHRODINGER EQUATIONS

This paper presents radial basis function (RBF) collocation methods for the coupled Klein-Gordon-Schrodinger equations. Unlike traditional mesh oriented methods, RBF collocation methods require only a scattered set of nodes in the domain where the solution is approximated. For the RBF collocation method in finite difference mode (RBF-FD), weights for the finite difference formula are obtained by solving local RBF interpolation problems set up around each node in the computational domain. We show that the RBF-FD method has good accuracy and a sparse coefficient matrix, as compared to the global form of the RBF collocation method and other methods.