• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Working paper

A Numerov-Crank-Nicolson-Strang scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip

arxiv.org. math. Cornell University, 2013. No. arxiv: 1307.5398.
Zlotnik A. A., Romanova A. V.
We consider an initial-boundary value problem for a 2D time-dependent Schrödinger equation on a semi-infi nite strip. For the Numerov-Crank-Nicolson finite-di fference scheme with discrete transparent boundary conditions, the Strang-type splitting with respect to the potential is applied. For the resulting method, the uniqueness of a solution and the uniform in time L_2-stability (in particular, L_2-conservativeness) are proved. Due to the splitting, an eff ective direct algorithm using FFT in the direction perpendicular to the strip is developed to implement the splitting method for general potential. Numerical results on the tunnel eff ect for smooth and rectangular barriers together with the practical error analysis on refining meshes are included as well.