Pointwise error estimates of a linearized difference scheme for strongly coupled fractional Ginzburg-Landau equations. (English) Zbl 1444.65049
Summary: In this paper, a linearized semi-implicit finite difference scheme is proposed to solve the strongly coupled fractional Ginzburg-Landau equations. The difference scheme, which involves three time levels, is unconditionally stable, fourth-order accurate in space, and second-order accurate in time. By using the energy method and mathematical induction, the unique solvability, the unconditional stability, and optimal pointwise error estimate are obtained. Finally, some numerical experiments are presented to validate our theoretical findings.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
| 26A33 | Fractional derivatives and integrals |
| 35Q56 | Ginzburg-Landau equations |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
Keywords:
fractional Laplacian; fourth-order convergence; Ginzburg-Landau equation; pointwise error estimate; unconditional stabilityReferences:
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