A Generalized Lyapunov-Sylvester Computational Method for Numerical Solutions of NLS Equation with Singular Potential
Year: 2017
Analysis in Theory and Applications, Vol. 33 (2017), Iss. 4 : pp. 333–354
Abstract
In the present paper a numerical method is developed to approximate the solution of two-dimensional Nonlinear Schrödinger equation in the presence of a singular potential. The method leads to generalized Lyapunov-Sylvester algebraic operators that are shown to be invertible using original topological and differential calculus issued methods. The numerical scheme is proved to be consistent, convergent and stable using the Lyapunov criterion, lax equivalence theorem and the properties of the generalized Lyapunov-Sylvester operators.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2017.v33.n4.4
Analysis in Theory and Applications, Vol. 33 (2017), Iss. 4 : pp. 333–354
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: NLS equation finite-difference scheme stability analysis Lyapunov criterion consistency convergence error estimates Lyapunov operator.
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