Volume 39, pp. 22-31, 2012.

Collocation methods based on radial basis functions for the coupled Klein-Gordon-Schrödinger equations

Ahmad Golbabai and Ali Safdari-Vaighani


This paper presents radial basis function (RBF) collocation methods for the coupled Klein-Gordon-Schrödinger 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.

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Key words

Collocation methods, coupled Klein-Gordon-Schrödinger equations, radial basis functions (RBF).

AMS subject classifications

65N06, 65N40, 65D25, 35Q51.

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