Alternating group explicit method for the dispersive equation

Unconditional stability of alternating difference schemes with intrinsic parallelism for the fourth-order parabolic equation

“…In 1999, Yuan et al [6] constructed the general schemes with intrinsic parallelism for two-dimensional parabolic systems, and gave the unconditionally stable analysis. More recently, the AGE scheme, the ASE-I scheme and the ASC-N scheme were extended to the dispersive equation and the nonlinear KdV equation in [7][8][9][10][11], and numerical results are satisfied.…”

“…Many effective methods have been presented in [1][2][3][4][5][6][7][8][9][10][11]. In 1983, Evans and Abdullah [1] observed that the alternate use of different schemes with truncation errors of opposite signs can lead to the cancelation of error terms at most points on the mesh lines, they first developed the Alternating Group Explicit (AGE) scheme for solving the parabolic equation.…”

An unconditionally stable alternating segment difference scheme of eight points for the dispersive equation

“…However, the parallel difference method for the equation has not been studied so much. Recently, Zhu Shao-hong et al presented the alternating group explicit (AGE) and alternating group explicit-implicit (AGEI) schemes for the initial-boundary value problem of the dispersive equation with the periodic boundary condition [17,18]. In this paper, we give a group of new asymmetric difference schemes to approach the dispersive equation, and we construct the alternating segment difference (ASD) scheme for the problem with this group of new asymmetric schemes.…”

Fourth-Order Accurate Alternating Group Schemes for the Diffusion Problem

“…Based on the works of Evans, B. L. Zhang develops the Alternating Segment Explicit-Implicit (ASEI) method and the Alternating Segment Crank-Nicolson (ASCN) method ( [3][4]). After that the study of the AGE scheme has been introduced into solving the hyperbolic equation and the dispersive equation respectively in [4] and [9]. All these methods are all unconditionally stable, and in space direction, their truncation errors are all nearly second order.…”