2018/05/31 by Dongdong He, Kejia Pan, He, Dongdong +1
Mathematics · #65M06 #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1805.12284
openalex publication_date 2018/05/31 · openalex created_date 2018/06/13 · openalex updated_date 2026/08/01
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.