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Volume 8, Issue 4
Optimal Error Estimates in Numerical Solution of Time Fractional Schrödinger Equations on Unbounded Domains

Zhi-Zhong Sun, Jiwei Zhang & Zhimin Zhang

DOI: 10.4208/eajam.190218.150718

East Asian J. Appl. Math., 8 (2018), pp. 634-655.

Published online: 2018-10

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  • Abstract

The artificial boundary method is used to reformulate the time fractional Schrödinger equation on the real line as a bounded problem with exact artificial boundary conditions. The problem appeared is solved by a numerical method employing the L1-formula for the Caputo derivative and finite differences for spatial derivatives. The convergence of the method studied and optimal error estimates in a special metric are obtained. The technique developed here can be also applied to study the convergence of approximation methods for standard Schrödinger equation.

  • Keywords

Time fractional Schrödinger equation, artificial boundary method, optimal error estimate, stability and convergence.

  • AMS Subject Headings

65M06, 35B65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-634, author = {Zhi-Zhong Sun, Jiwei Zhang and Zhimin Zhang}, title = {Optimal Error Estimates in Numerical Solution of Time Fractional Schrödinger Equations on Unbounded Domains}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {4}, pages = {634--655}, abstract = {

The artificial boundary method is used to reformulate the time fractional Schrödinger equation on the real line as a bounded problem with exact artificial boundary conditions. The problem appeared is solved by a numerical method employing the L1-formula for the Caputo derivative and finite differences for spatial derivatives. The convergence of the method studied and optimal error estimates in a special metric are obtained. The technique developed here can be also applied to study the convergence of approximation methods for standard Schrödinger equation.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.190218.150718}, url = {http://global-sci.org/intro/article_detail/eajam/12812.html} }
TY - JOUR T1 - Optimal Error Estimates in Numerical Solution of Time Fractional Schrödinger Equations on Unbounded Domains AU - Zhi-Zhong Sun, Jiwei Zhang & Zhimin Zhang JO - East Asian Journal on Applied Mathematics VL - 4 SP - 634 EP - 655 PY - 2018 DA - 2018/10 SN - 8 DO - http://doi.org/10.4208/eajam.190218.150718 UR - https://global-sci.org/intro/article_detail/eajam/12812.html KW - Time fractional Schrödinger equation, artificial boundary method, optimal error estimate, stability and convergence. AB -

The artificial boundary method is used to reformulate the time fractional Schrödinger equation on the real line as a bounded problem with exact artificial boundary conditions. The problem appeared is solved by a numerical method employing the L1-formula for the Caputo derivative and finite differences for spatial derivatives. The convergence of the method studied and optimal error estimates in a special metric are obtained. The technique developed here can be also applied to study the convergence of approximation methods for standard Schrödinger equation.

Zhi-Zhong Sun, Jiwei Zhang and Zhimin Zhang. (2018). Optimal Error Estimates in Numerical Solution of Time Fractional Schrödinger Equations on Unbounded Domains. East Asian Journal on Applied Mathematics. 8 (4). 634-655. doi:10.4208/eajam.190218.150718
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