In this paper, we present and analyze fully discrete finite difference schemes designed for
solving the initial value problem associated with the fractional Korteweg-de Vries (KdV) …

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 …

In this paper, we study the stability and convergence of a fully discrete finite difference
scheme for the initial value problem associated with the Korteweg-De Vries (KdV) equation …

We propose a local discontinuous Galerkin (LDG) method for fractional Korteweg-de Vries
equation involving the fractional Laplacian with exponent $\alpha\in (1, 2) $ in one and two …

In this paper, a fourth-order finite difference scheme that preserves the dissipation of energy
for solving the 2D Benjamin-Bona-Mahony-Burgers (BBMB) equation is proposed. The …

In this work, an exact solitary wave solution and a linear conservative difference scheme for
solving the generalized Korteweg–de Vries–Kawahara (GKdV-K) equation are proposed …

In this work, based on the value computed by the fourth-order implicit Padé scheme for the
first derivative, a fourth-order three-point compact scheme for approximating the third …

A compact difference operator is a valuable technique which has been used to develop
numerical schemes capable of solving various types of differential equations. Advantages of …

In this article, we present two high-order structure-preserving difference schemes for the
modified Kawahara equation, which are named as Scheme I and Scheme II, respectively …

In this paper, the difference method with intrinsic parallelism is studied in order to meet the
needs of quickly solving the variable-coefficient compound KdV-Burgers equation. The …