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

Abstract

SUMMARYA group of new Saul'yev-type asymmetric difference schemes to approach the dispersive equation are given here. On the basis of these schemes, an alternating difference scheme with intrinsic parallelism for solving the dispersive equation is constructed. The scheme is unconditionally stable. Numerical experiments show that the method has high accuracy.

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.…”

Unconditional stability of alternating difference schemes with variable time steplengthes for dispersive equation

“…Many powerful methods have been presented in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]20]. In 1983, Evans and Abdullah [1] observed that the alternate use of different schemes with truncation errors of opposite signs can implement the parallel computation and has high accuracy and unconditional stability.…”

A finite difference alternating segment scheme of parallel computations for solving heat equation

“…The basic idea behind this calculation is that the solution process can be divided into smaller subsections, therefore when these subsections are calculated simultaneously the main problem is solved in a shorter time. The alternating schemes [2,7,10,11,15,16,17,19] and the domain decomposition schemes [3,13,14] are two major types of parallel calculation. The alternating schemes are unconditionally stable and intrinsically parallel.…”