A Generalized Lyapunov-Sylvester Computational Method for Numerical Solutions of NLS Equation with Singular Potential

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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