In this paper,the multigrid method is presented associated with LUSGS implicit scheme to calculating the low speed flow field around the NLR7301 case#1 and the transonic flow field around the DLRF4 wing-body configuration,all results conf.

An efficient numerical method that contains the new LU type implicit scheme and the modified fourth order high resolution MUSCL TVD scheme is proposed for solving the compressible Navier Stokes equations.

A new implicit scheme based on the LU-SGS scheme in conjunction with diagonalization and Cramer s rule (LUSGS-DC) has been developed for solving the compressibleNavier-Stokes equations.

Computing classical trajectories of H_2 system by symplectic scheme;

Two order two stage explicit symplectic scheme and its stablity for the four-order rod vibration equation;

Computing one-dimensional stationary state Schrdinger equation by Symplectic schemes;

Multi-symplectic equations with multi-symplectic schemes which must preserve discrete multi-symplectic conservation law was discreted.

We consider a multi-symplectic scheme for the SRLW equation in the paper.

And the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior .

In this paper, we will present the implicit symplectic schemes of the four-order rod vibration equation via tanh(x) and the corresponding iterative methods.

In this paper,we will use the hyperbolic functions sinh(x)and tanh(x)toconstruct symplectic schemes of arbitrary order for schrodinger equations and stabilities ofthese constructed schemes are also discussed.