In this paper, a fourth-order compact and energy conservative difference scheme is
proposed for solving the two-dimensional nonlinear Schrödinger equation with periodic …

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 …

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, a high order finite difference scheme for a two dimensional fractional Klein–
Gordon equation subject to Neumann boundary conditions is proposed. The difficulty …

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 focus of this paper is on the optimal error bounds of two finite difference schemes for
solving the d-dimensional (d= 2, 3) nonlinear Klein-Gordon-Schrödinger (KGS) equations …

The paper focuses on numerical study of the time-dependent Ginzburg–Landau (TDGL)
equations under the Lorentz gauge. The proposed method is based on a fully linearized …

In this work, we revisit the adaptive L1 time-stepping scheme for solving the time-fractional
Allen-Cahn equation in the Caputo's form. The L1 implicit scheme is shown to preserve a …