Finite difference parallel schemes based on follow-flow scheme for KdV equation

A group of Saul´yev asymmetric difference schemes based on follow-flow scheme to approach KdV equation is given here. Using these new asymmetric difference schemes, we construct the parallel alternating group schemes based on follow-flow scheme, which are absolutely stable by analysis of linearization procedure. Numerical experiments for the cases of single soliton solution and double soliton solution are performed, which show that the accuracy and stability of the schemes are better than parallel algorithms existed.