WIAS Preprint No. 1446, (2009)

Numerical algorithms for Schrödinger equation with artificial boundary conditions



Authors

  • Čiegis, Raimondas
  • Laukaitytė, Inga
  • Radziunas, Mindaugas

2010 Mathematics Subject Classification

  • 65M06 65M12 35Q40

Keywords

  • finite difference method, Schrödinger problem, absorbing boundary conditions, transparent boundary conditions, numerical experiments

Abstract

We consider a one-dimensional linear Schrödinger problem defined on an infinite domain and approximated by the Crank-Nicolson type finite difference scheme. To solve this problem numerically we restrict the computational domain by introducing the reflective, absorbing or transparent artificial boundary conditions. We investigate the conservativity of the discrete scheme with respect to the mass and energy of the solution. Results of computational experiments are presented and the efficiency of different artificial boundary conditions is discussed.

Appeared in

  • Numer. Funct. Anal. Optim., 30 (2009) pp. 903--923.

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