Weighted essentially non-oscillatory schemes are described in detail for a total variation-based image restoration problem with Gaussian kernel at different boundary conditions.Numerical results with three methods (weighted essentially non-oscillatory schemes,wiener algorithm and a combination of them) are compared. Experimental results demonstrate effectiveness of the combination of weighted essentially non-oscillatory schemes and wiener algorithm.

A new conservative difference scheme is proposed for nonlinear Schrödinger equation, and its convergence and stability are proved. By means of numerical computing, the discretization for nonlinear term of nonlinear Schrödinger equation is discussed, and it is followed that the new difference scheme is better than the scheme of paper[7] which is a special case of the new scheme in precision, when suitable parameter is adopted.

A scheme is outlined for solving hyperbolic conservation laws by finite element method of piecewise linear interpolations. It is different from the discontinuous finite element on the boundaries of neighboring cells to solve Riemann problems that the scheme is designed to solve hyperbolic conservation laws based on the Hamilton Jacobi equations. Under the CFL condition, the scheme is proved that it satisfies the maximal principle and is a TVD scheme. Numerical examples are given and discussed.

A finite difference of energy conservation is proposed for nonlinear Klein Gordon (NKG) equation.Its convergence and stability have been proved.Results of numerical computation are also analysed.

A modified algebraic multigrid (AMG) method for queueing networks is presented.The method keeps the singularing of queueing networks by modifying the restriction operators.Numerical results indicate that this method is more efficient and robust than conventional AMG method.

A new algorithm of algebraic multigrid (AMG)method is proposed.As an important example, the AMG method is applied to solve the splitting scheme of the Euler equations.The equations with high CFL number can be calculated with the AMG method.This example demonstrates that the AMG method can solve the linear algebraic systems of equations unable to be solved by Gauss-Seidel iteration method.This is a new result and extends the range of application of the AMG method.

In this paper, we present a new interpolation formula of algebraic multigrid (AM G). The AMG algorithm with this formula can solve many problems, even very ill-conditioned problems like biharmonic equation and convection-diffusion equation with discontinuous coefficient etc. The theoretical analysis and numerical experiments demonstrate that this formula is very robust and efficient, so we have extended the application range of AMG.

In this paper, We consider solitary waves induced by boundary pulses for regularized Long-wave equation. A conservative difference scheme is presented for the equation. Using the scheme, solitary waves induced by several boundary pulses are computed numerically. We explore the relationship between the amplitudes and numbers of the solitons produced and the boundary pulses, and compare solitons induced by the boundary pulse with ones produced ny initial pulses.