Construction of discretization schemes, convergence principle, strongly convergent scheme and weakly convergent scheme for stochastic differential equations as well as computing method of jump stochastic differential equation are presented. Related partial differential equations are solved by probability method. Finally several examples in application are given.

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.

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.