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Convergence of an Eighth-Order Compact Difference Scheme for the Nonlinear Schrödinger Equation
Author
Source
Advances in Numerical Analysis
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-24, 24 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-10-17
Country of Publication
Egypt
No. of Pages
24
Main Subjects
Abstract EN
A new compact difference scheme is proposed for solving the nonlinear Schrödinger equation.
The scheme is proved to conserve the total mass and the total energy and the optimal convergent rate, without any restriction on the grid ratio, at the order of O(h8+τ2) in the discrete L∞-norm with time step τ and mesh size h.
In numerical analysis, beside the standard techniques of the energy method, a new technique named “regression of compactness” and some lemmas are proposed to prove the high-order convergence.
For computing the nonlinear algebraical systems generated by the nonlinear compact scheme, an efficient iterative algorithm is constructed.
Numerical examples are given to support the theoretical analysis.
American Psychological Association (APA)
Wang, Tingchun. 2012. Convergence of an Eighth-Order Compact Difference Scheme for the Nonlinear Schrödinger Equation. Advances in Numerical Analysis،Vol. 2012, no. 2012, pp.1-24.
https://search.emarefa.net/detail/BIM-507587
Modern Language Association (MLA)
Wang, Tingchun. Convergence of an Eighth-Order Compact Difference Scheme for the Nonlinear Schrödinger Equation. Advances in Numerical Analysis No. 2012 (2012), pp.1-24.
https://search.emarefa.net/detail/BIM-507587
American Medical Association (AMA)
Wang, Tingchun. Convergence of an Eighth-Order Compact Difference Scheme for the Nonlinear Schrödinger Equation. Advances in Numerical Analysis. 2012. Vol. 2012, no. 2012, pp.1-24.
https://search.emarefa.net/detail/BIM-507587
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-507587