An efficient fourth-order in space difference scheme for the nonlinear fractional Ginzburg-Landau equation

作者：Wang, Pengde; Huang, Chengming^*

来源：BIT Numerical Mathematics, 2018, 58(3): 783-805.

DOI：10.1007/s10543-018-0698-9

• Fractional Ginzburg-Landau equation
• Riesz fractional derivative
• Implicit-explicit method
• Fractional compact scheme
• Convergence

This paper proposes and analyzes a high-order implicit-explicit difference scheme for the nonlinear complex fractional Ginzburg-Landau equation involving the Riesz fractional derivative. For the time discretization, the second-order backward differentiation formula combined with the explicit second-order Gear's extrapolation is adopted. While for the space discretization, a fourth-order fractional quasi-compact method is used to approximate the Riesz fractional derivative. The scheme is efficient in the sense that, at each time step, only a linear system with a coefficient matrix independent of the time level needs to be solved. Despite of the explicit treatment of the nonlinear term, the scheme is shown to be unconditionally convergent in the l2 h norm, semi-H-h(alpha/2) norm and l(h)(infinity) norm at the order of O(tau(2) + h(4)) with tau time step and h mesh size. Numerical tests are provided to confirm the accuracy and efficiency of the scheme.

• 出版日期2018-9
• 单位河南财经政法大学; 华中科技大学