Optimal Error Estimates in Numerical Solution of Time Fractional Schrödinger Equations on Unbounded Domains
Year: 2018
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.190218.150718
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 634–655
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Time fractional Schrödinger equation artificial boundary method optimal error estimate stability and convergence.