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Volume 33, Issue 4
A Generalized Lyapunov-Sylvester Computational Method for Numerical Solutions of NLS Equation with Singular Potential

Riadh Chteoui & Anouar Ben Mabrouk

DOI: 10.4208/ata.2017.v33.n4.4

Anal. Theory Appl., 33 (2017), pp. 333-354.

Published online: 2017-11

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  • 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.

  • Keywords

NLS equation, finite-difference scheme, stability analysis, Lyapunov criterion, consistency, convergence, error estimates, Lyapunov operator.

  • AMS Subject Headings

35B05, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-33-333, author = {Riadh Chteoui and Anouar Ben Mabrouk}, title = {A Generalized Lyapunov-Sylvester Computational Method for Numerical Solutions of NLS Equation with Singular Potential}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {33}, number = {4}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2017.v33.n4.4}, url = {http://global-sci.org/intro/article_detail/ata/10701.html} }
TY - JOUR T1 - A Generalized Lyapunov-Sylvester Computational Method for Numerical Solutions of NLS Equation with Singular Potential AU - Riadh Chteoui & Anouar Ben Mabrouk JO - Analysis in Theory and Applications VL - 4 SP - 333 EP - 354 PY - 2017 DA - 2017/11 SN - 33 DO - http://doi.org/10.4208/ata.2017.v33.n4.4 UR - https://global-sci.org/intro/article_detail/ata/10701.html KW - NLS equation, finite-difference scheme, stability analysis, Lyapunov criterion, consistency, convergence, error estimates, Lyapunov operator. AB -

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.

Riadh Chteoui and Anouar Ben Mabrouk. (2017). A Generalized Lyapunov-Sylvester Computational Method for Numerical Solutions of NLS Equation with Singular Potential. Analysis in Theory and Applications. 33 (4). 333-354. doi:10.4208/ata.2017.v33.n4.4
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