Galerkin methods for the Davey-Stewartson equations. (English) Zbl 1427.65246
Summary: In this paper, we propose two Galerkin methods to investigate the evolution of the Davey-Stewartson equations. The extrapolated Crank-Nicolson scheme and decoupled semi-implicit multistep scheme are employed to increase the order of the time discrete accuracy, which only requires the solutions of a linear system at each time step. Four numerical experiments are presented to illustrate the features of the proposed numerical methods, such as the optimal convergence order, the conservation variable and the application in rogue waves.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
Keywords:
Davey-Stewartson equations; Galerkin finite element method; extrapolated Crank-Nicolson method; explicit multistep methodReferences:
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