Journal
NUMERICAL ALGORITHMS
Volume 76, Issue 4, Pages 939-958Publisher
SPRINGER
DOI: 10.1007/s11075-017-0291-3
Keywords
Optical solitons; Space-fractional Schrodinger equations; Gross-Pitaevskii equation; Exponential operator splitting; Local extrapolation
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An efficient local extrapolation of the exponential operator splitting scheme is introduced to solve the multi-dimensional space-fractional nonlinear Schrodinger equations. Stability of the scheme is examined by investigating its amplification factor and by plotting the boundaries of the stability regions. Empirical convergence analysis and calculation of the local truncation error exhibit the second-order accuracy of the proposed scheme. The performance and reliability of the proposed scheme are tested by implementing it on two- and three-dimensional space-fractional nonlinear Schrodinger equations including the space-fractional Gross-Pitaevskii equation, which is used to model optical solitons in graded-index fibers.
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