Year: 2014
Author: F. J. Gaspar, C. Rodrigo, R. Ciegis, A. Mirinavicius
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 1 : pp. 131–147
Abstract
This paper deals with the numerical solution of both linear and non-linear Schrödinger problems, which mathematically model many physical processes in a wide range of applications of interest. In particular, a comparison of different solvers and different approaches for these problems is developed throughout this work. Two finite difference schemes are analyzed: the classical Crank-Nicolson approach, and a high-order compact scheme. Solvers based on geometric multigrid, Fast Fourier Transform and Alternating Direction Implicit methods are compared. Finally, the efficiency of the considered solvers is tested for a linear Schrödinger problem, proving that the computational experiments are in good agreement with the theoretical predictions. In order to test the robustness of the MG solver two additional Schrödinger problems with a nonconstant potential and nonlinear right-hand side are solved by the MG solver, since the efficiency of this solver depends on such data.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2014-IJNAM-518
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 1 : pp. 131–147
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: finite difference method Schrödinger problem multigrid method Alternating Direction Implicit method Fast Fourier Transform method.