A numerical method for two-dimensional Schrödinger equation using collocation and radial basis functions

@article{Dehghan2007ANM,
  title={A numerical method for two-dimensional Schr{\"o}dinger equation using collocation and radial basis functions},
  author={Mehdi Dehghan and Ali Shokri},
  journal={Computers & Mathematics with Applications},
  year={2007},
  volume={54},
  pages={136-146}
}
In this paper, we propose a numerical scheme to solve the two-dimensional (2D) time-dependent Schrödinger equation using collocation points and approximating the solution using multiquadrics (MQ) and the Thin Plate Splines (TPS) Radial Basis Function (RBF). The scheme works in a similar fashion as finite-difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme. c © 2007 Elsevier Ltd… CONTINUE READING

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