A fourth-order implicit-explicit scheme for the space fractional nonlinear Schrodinger equations

作者：Khaliq, A. Q. M.^*; Liang, X.; Furati, K. M.

来源：Numerical Algorithms, 2017, 75(1): 147-172.

DOI：10.1007/s11075-016-0200-1

• Space fractional nonlinear Schrodinger equations
• Riesz fractional derivative
• Implicit-explicit scheme
• Compact scheme
• Exponential time differencing

A fourth-order implicit-explicit time-discretization scheme based on the exponential time differencing approach with a fourth-order compact scheme in space is proposed for space fractional nonlinear Schrodinger equations. The stability and convergence of the compact scheme are discussed. It is shown that the compact scheme is fourth-order convergent in space and in time. Numerical experiments are performed on single and coupled systems of two and four fractional nonlinear Schrodinger equations. The results demonstrate accuracy, efficiency, and reliability of the scheme. A linearly implicit conservative method with the fourth-order compact scheme in space is also considered and used on the system of space fractional nonlinear Schrodinger equations.

• 出版日期2017-5
• 单位湖北文理学院; 中国石油大学（北京）