A time dependent model for deblurring and denoising problems is proposed.Comparisons with the Rudin-Osher-Fatemi model are made in numerical experiments with antireflective boundary conditions and medium boundary conditions.The results demonstrate that the error with medium boundary conditions is smaller than that with antireflective boundary conditions.

A model of image processing for anisotropic diffusion driven by diffusion tensors is investigated. An implicit difference scheme is constructed. A large sparse matrix with 13 diagonals is formed with which general iterative methods don't work well. With algebraic multi-grid method (AMG), linear system of equations are solved.Numerical experiments are shown.

Particular solution BEM is used to solve three-dimensional Pennes equation.The solution is devided into the common solution of Poisson equation and the particular solution.The common solution is solved by BEM while the particular solution is given by the method of separation of variables.Temperature and heatflux are computed piecewisely in each time step and then the value on the nods in the field is computed.Numerical simulation of cancer hypothermia is given based on this method.

A new approach for producing the MG interpolatory formula is proposed on the basis of the defect equation. This new interpolatory formula makes full use of information of coarser grids, and thus has higher accuracy. Numerical experiments for Poisson equation, anisotropic equation, biharmonic equation, and even 3D problem show that the new interpolatory formula improves the asymptotic convergence rate, and reduces the storage capacity and computational time for the AMG method.

A new finite difference scheme is proposed for radial symmetric nonlinear Schrödinger equation. This is a scheme of three levels which needn't to iterate. Thus, the new scheme requires less CPU time. Convergence and stability of the new scheme are proved. By means of numerical computation, it is followed that the new scheme is efficient.

The splitting difference scheme is used to study flow separation. Flows behind a Circular Cylinder are computed as a model problem. In view of the nature of the flows, the variables are transformed. The boundary condition for pressure is given by intermediate velocity. The velocity boundary Conditions on the rigid wall of free-slip are given by interpolation. The multigrid algorithm is applied to the Pressure iteration. We also Choose better initial Values for the model problem by means of the multigrid algorithm idea.

The process of forming of Self Forging Fragment (SFF for short) is a very complicated problem of explosion. Because of SFF is axisymmetric, 2-d imentional elastic-plastic mechnical equations are used to discribe this process. In solving these equations, we use integral definitions of the partial derivatives by M.L. Wilkins,and Lagrange quadrilateral grid.The shape of the SFF obtained from our 2-dimensional numerical simulation compares fairly with that in the high speed x-ray photogragh of the actural experimental process.