This paper is concerned with the construction and analysis of a novel linearized compact
ADI scheme for the two-dimensional Riesz space fractional nonlinear reaction–diffusion …

The main aim of this paper is to construct an efficient Galerkin–Legendre spectral
approximation combined with a finite difference formula of L 1 type to numerically solve the …

In this paper, we present a fully discrete and structure-preserving scheme for the nonlinear
fractional Schrödinger equations. The key is to introduce a scalar auxiliary variable and …

Mass and energy conservative numerical methods are proposed for a general system of N
strongly coupled nonlinear Schrödinger equations (N-CNLS). Motivated by the structure …

In recent years, various types of methods have been proposed to approximate the Caputo
fractional derivative numerically. A common challenge of the methods is the non-local …

The formulation of the Local Discontinuous Galerkin (LDG) method applied to the space
fractional Klein-Gordon-Schrödinger system with generalized interaction is presented. By …

In this manuscript, we consider an efficient dissipation-preserving finite element method for a
class of two-dimensional nonlinear fractional wave equations on irregular convex domains …

Fast high-order compact finite difference schemes are investigated for solving the two-
dimensional nonlinear Schrödinger equation with periodic boundary conditions. These …

In this paper, we develop an implicit difference method for solving the nonlinear time-space
fractional Schrödinger equation. The scheme is constructed by using the L2-1 σ formula to …

In this paper, a novel auxiliary variable approach is firstly introduced to reformulate the
fractional nonlinear Schrödinger equation with wave operator in an equivalent system …