A FOURTH-ORDER COMPACT ADI SCHEME FOR TWO-DIMENSIONAL NONLINEAR SPACE FRACTIONAL SCHRODINGER EQUATION

作者：Zhao, Xuan^*; Sun, Zhi-Zhong; Hao, Zhao-Peng

来源：SIAM Journal on Scientific Computing, 2014, 36(6): A2865-A2886.

DOI：10.1137/140961560

• fourth-order compact operator
• nonlinear space fractional Schrodinger equation
• Riesz derivative
• fractional Laplacian
• solvability
• convergence

In this paper, a novel compact operator is derived for the approximation of the Riesz derivative with order alpha is an element of (1, 2]. The compact operator is proved with fourth-order accuracy. Combining the compact operator in space discretization, a linearized difference scheme is proposed for a two-dimensional nonlinear space fractional Schrodinger equation. It is proved that the difference scheme is uniquely solvable, stable, and convergent with order O(tau(2) + h(4)), where tau is the time step size, h = max{h(1), h(2)}, and h(1), h(2) are space grid sizes in the x direction and the y direction, respectively. Based on the linearized difference scheme, a compact alternating direction implicit scheme is presented and analyzed. Numerical results demonstrate that the compact operator does not bring in extra computational cost but improves the accuracy of the scheme greatly.

• 出版日期2014
• 单位东南大学