The propagation of nonlinear water waves under complex wave conditions is the key issue hydrodynamics both in coastal and ocean engineering, which significant prediction strongly phenomena regarding wave–structure interactions. In present study, meshless generalized finite difference method (GFDM) together with second-order Runge–Kutta (RKM2) employed to construct a fully three-dimensional (3D)...

In this paper, we propose a three-level linearized implicit difference scheme for the two-dimensional spatial fractional nonlinear complex Ginzburg-Landau equation. We prove that is stable and convergent under mild conditions. The optimal convergence order $\mathcal {O}(\tau ^{2}+{h_{x}^{2}}+{h_{y}^{2}})$ obtained in pointwise sense by developing new Sobolev imbedding inequality based on work K...