Nonlinear evolution equations are widely used to describe nonlinear phenomena in natural
and social sciences. However, they are usually quite difficult to solve in most instances. This …

This paper proposes and analyzes an efficient difference scheme for the nonlinear complex
Ginzburg–Landau equation involving fractional Laplacian. The scheme is based on the …

Abstract Space and time approximations for two-dimensional space fractional complex
Ginzburg–Landau equation are examined. The schemes under consideration are discreted …

In this paper, we propose a linearized implicit finite difference scheme for solving the
fractional Ginzburg-Landau equation. The scheme, which involves three time levels, is …

This paper proposes and analyzes a high-order implicit-explicit difference scheme for the
nonlinear complex fractional Ginzburg–Landau equation involving the Riesz fractional …

Abstract Delay Sobolev equations (DSEs) are a class of important models in fluid
mechanics, thermodynamics and the other related fields. For solving this class of equations …

In this paper, we present a fourth-order difference scheme for solving the Allen-Cahn
equation in both 1D and 2D. The proposed scheme is described by the compact difference …

The numerical solution for the one‐dimensional complex fractional Ginzburg–Landau
equation is considered and a linearized high‐order accurate difference scheme is derived …

This study aims to investigate some theoretical results, numerical study and a real-word
application of the SFGLE, involving the fractional Laplacian. First, we describe the …

In this paper, the second-order weighted implicit-explicit (IMEX) finite element method (FEM)
is presented for the nonlinear Ginzburg-Landau equation (GLE). We mainly focus on a …