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Multidimensional problems for general coupled systems of time-space fractional Schrödinger equations

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In the present paper, general coupled system of nonlinear time-space fractional Schrödinger equations is considered in multi-dimensional case. Finite difference method is used to construct the difference schemes for one and multidimensional problems for general coupled system of nonlinear time-space fractional Schrödinger equations. A reformulation of Grünwald-Letnikov difference derivative is used to construct the difference schemes. Convergence and stability results are presented. Numerical experiments are carried out on problems with one and two dimensional space variables.
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Keywords: FINITE DIFFERENCE METHOD; GENERAL COUPLED SYSTEM OF FRACTIONAL SCHRÖDINGER EQUATION; MULTIDIMENSIONAL DIFFERENTIAL PROBLEM; RIESZ FRACTIONAL DERIVATIVE

Document Type: Research Article

Publication date: June 1, 2018

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