A fourth-order difference scheme for the fractional nonlinear Schrödinger equation with wave operator. (English) Zbl 1490.65159
Summary: In this paper, an efficient semi-implicit difference scheme for solving the fractional nonlinear Schrödinger equation with wave operator are proposed and analyzed. The semi-implicit scheme involves three-time levels, is unconditionally stable and fourth-order accurate in space and second-order accurate in time. Furthermore, the unique solvability, unconditional stability and convergence of the method in the \(L^\infty\)-norm are proved rigorously by the energy method. Finally, numerical experiments are presented to confirm our theoretical results.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
nonlinear Schrödinger equation; fractional Laplacian; wave operator; unconditional stability; semi-implicit difference schemeReferences:
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