Geodesic
Collocation methods based on radial basis functions for the coupled Klein-Gordon-Schrödinger equations
Electronic transactions on numerical analysis, Tome 39 (2012), pp. 22-31.

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Summary: 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.
Classification : 65N06, 65N40, 65D25, 35Q51
Keywords: collocation methods, coupled Klein-Gordon-Schrödinger equations, radial basis functions (RBF) 
@article{ETNA_2012__39__a24,
     author = {Golbabai, Ahmad and Safdari-Vaighani, Ali},
     title = {Collocation methods based on radial basis functions for the coupled {Klein-Gordon-Schr\"odinger} equations},
     journal = {Electronic transactions on numerical analysis},
     pages = {22--31},
     publisher = {mathdoc},
     volume = {39},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2012__39__a24/}
}
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Golbabai, Ahmad; Safdari-Vaighani, Ali. Collocation methods based on radial basis functions for the coupled Klein-Gordon-Schrödinger equations. Electronic transactions on numerical analysis, Tome 39 (2012), pp. 22-31. http://geodesic.mathdoc.fr/item/ETNA_2012__39__a24/