The locally extrapolated exponential splitting scheme for multi-dimensional nonlinear space-fractional Schrödinger equations

An efficient local extrapolation of the exponential operator splitting scheme is introduced to solve the multi-dimensional space-fractional nonlinear Schrödinger 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 Schrödinger equations including the space-fractional Gross-Pitaevskii equation, which is used to model optical solitons in graded-index fibers.