Spectral approximation for nonlinear time fractional Schrödinger equation on graded meshes

This paper is concerned with the numerical approximation of the nonlinear time fractional Schrödinger equation subject to the initial and Neumann boundary conditions whose solution exhibits an initial weak singularity. A linearized fully discrete scheme is presented by using the finite difference me...

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Bibliographic Details
Published inInternational journal of computer mathematics Vol. 99; no. 12; pp. 2524 - 2541
Main Authors Chen, Li, Lü, Shujuan
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.12.2022
Taylor & Francis Ltd
Subjects
Approximation
Boundary conditions
convergence
Discretization
Finite difference method
Mathematical analysis
Schrodinger equation
spectral method
Spectral methods
Time fractional Schrödinger equation
weak singularity
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Summary:This paper is concerned with the numerical approximation of the nonlinear time fractional Schrödinger equation subject to the initial and Neumann boundary conditions whose solution exhibits an initial weak singularity. A linearized fully discrete scheme is presented by using the finite difference method on graded meshes for temporal discretization and Gauss Lobatto Legendre Birkhoff spectral method for spatial discretization. Based on a temporal-spatial error splitting argument, the boundedness of the numerical solution in the norm is proved rigorously. The convergence of the proposed scheme is obtained unconditionally. The theoretical results are verified through some numerical examples.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2022.2070842