Journal
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
Volume 97, Issue 11, Pages 2259-2286Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160.2019.1692200
Keywords
Time fractional Schrodinger equation; WSGL difference operator; Z-transform; stability; Sinc-Galerkin method
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Funding
- NationalNatural Science Foundation of China [11426174, 11702214]
- Natural Science Basic Research Plan in Shaanxi Province of China [2018JM1016]
- National Natural Science Foundation of China [11972286]
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In this paper, high order time discretization schemes for time fractional Schrodinger equations in one and two dimensions are proposed. Our schemes are based on high order weighted and shifted Grunwald-Letnikov (WSGL) difference operators for the time fractional derivatives, Sinc-Galerkin methods are used for the space variables. The stability of time semi-discrete schemes is analysed with the help of -transform. For the fully discretization schemes, the standard Sinc-Galerkin method and symmetric Sinc-Galerkin method are established by selecting proper weight functions. Finally, we apply our numerical schemes to solve one-dimensional and two-dimensional time fractional Schrodinger equations, verify the validity of present numerical schemes.
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