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 …

In this paper, an effective linearized element-free Galerkin (EFG) method is developed for
the numerical solution of the complex Ginzburg–Landau (GL) equation. To deal with the time …

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 …

In this paper, we first construct an appropriate new generating function, and then based on
this function, we establish a fourth-order numerical differential formula approximating 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 …

The Ginzburg–Landau equation has been used as a mathematical model for various pattern
formation systems in mechanics, physics and chemistry. In this paper, we study the complex …

In this paper, we solve the coupled Ginzburg-Landau equations by using a linearized
variable-time-step second order backward differentiation formula in time combining with a …

Over the years, energy-dissipation-preserving (EDP) numerical methods (EDP-NMs) for the
nonlinear system of energy dissipation have attracted considerable attention because they …

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