A three-level linearized difference scheme for the coupled nonlinear fractional Ginzburg-Landau equation
For researchers in numerical analysis and fractional PDEs, this provides a stable and accurate numerical method for a previously unaddressed coupled system.
This paper proposes a linearized implicit finite difference scheme for the coupled fractional Ginzburg-Landau equations, achieving unconditional stability and second-order accuracy in time and space. Numerical results confirm the theoretical analysis.
In this paper, the coupled fractional Ginzburg-Landau equations are first time investigated numerically. A linearized implicit finite difference scheme is proposed. The scheme involves three time levels, is unconditionally stable and second-order accurate in both time and space variables. The unique solvability, the unconditional stability and optimal pointwise error estimates are obtained by using the energy method and mathematical induction. Moreover, the proposed second-order method can be easily extended into the fourth-order method by using an average finite difference operator for spatial fractional derivatives and Richardson extrapolation for time variable. Finally, numerical results are presented to confirm the theoretical results.