The use of compact boundary value method for the solution of two-dimensional Schrödinger equation

  • Authors:
  • Akbar Mohebbi;Mehdi Dehghan

  • Affiliations:
  • Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave.,15914, Tehran, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave.,15914, Tehran, Iran

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2009

Quantified Score

Hi-index 7.33

Visualization

Abstract

In this paper, a high-order and accurate method is proposed for solving the unsteady two-dimensional Schrodinger equation. We apply a compact finite difference approximation of fourth-order for discretizing spatial derivatives and a boundary value method of fourth-order for the time integration of the resulting linear system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables. Moreover this method is unconditionally stable due to the favorable stability property of boundary value methods. The results of numerical experiments are compared with analytical solutions and with those provided by other methods in the literature. These results show that the combination of a compact finite difference approximation of fourth-order and a fourth-order boundary value method gives an efficient algorithm for solving the two dimensional Schrodinger equation.