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

  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},
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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Multiquadrics – A scattered data approximation scheme with applications to computational fluid dynamics – II

E. J. Kansa
Comput. Math. Appl. 19 (1990) 147–161. 146 M. Dehghan, A. Shokri / Computers and Mathematics with Applications 54 • 2007
View 1 Excerpt

The one-dimensional heat equation subject to a boundary integral specification

M. Dehghan
Chaos Solitons Fractals 32 • 2007
View 1 Excerpt

A semi-discrete higher order compact scheme for the unsteady two-dimensional Schrödinger equation

J. C. Kalita, P. Chhabra, S. Kumar
J. Comput. Appl. Math. 197 • 2006
View 3 Excerpts

Fully explicit finite-difference methods for two-dimensional diffusion with an integral condition

M. Dehghan
Nonlinear Anal., TMA 48 (5(A)) • 2002
View 1 Excerpt

Fully explicit finitedifference methods for two - dimensional diffusion with an integral condition , Nonlinear Anal

M. Dehghan

On the finite-difference schemes for the numerical solution of two dimensional Schrödinger equation

M. Subaşi
Numer. Methods Partial Differential Equations 18 • 2002
View 2 Excerpts

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