A synthetic description on numerical methods is given for calculating periodic solutions of autonomous ordinary differentical equaitons.It focuses on the introductions of original structural ideas and processes of the methods or algorithms.

Energy cost that bounce shock wave on its propagation through outer iron core must pay for dissociation of heavy nuclei is considered as an adjusted parameter. Based on this, the method of artificial prompt explosion model is proposed to research effects of iron core mass of SN Ⅱ on prompt explosion. Range of iron core mass of presuperonva models which can produce prompt explosion is estimatd. The preliminary investsgation shows that iron core mass of presupermova models of WW(1993) is too large to produce prompt explosion.

The(0.74-0.91)M_⊙ of the iron core of Supernovae is a very important region of convective instability,which is found through the present numerical simulation.

This paper describes a new and pure Lagrangian method——called "Smoothed Particle Hy drodynamics" (SPH) method. The method is to actually evaluate spatial gradients without the use of any grid. Thus it does not suffer form the severe problems always associated with mesh tangling and distortion. Therefore it can be applied to multidimensional hydrodynamics which could effectively model three-dimensional systems which lack symmetry and possess large voids. At first, the paper gives an introduction to theoretical basis to SPH. Emphasis is given to a proper derivation of the SPH equations from the hydrodynamical conservation equations. Discussion covers some relative problems such as artifical viscosity, thermal conduction, self-gravity and sink and magnetic fields, choosing the smoothing kernels, and implementation of SPH code, etc.

The objective of this study is to develop a mathematical model for calculating the initiation and spresd of fire resulting from an attack on an urban area, and to apply the model for predicting the fire-depentdent fire damage to an assumed city. The numerical test is obtained valuable information by using the parameters of fire spread from Japanese Hiroshima.The model to be developed is included——to determine description for a simplified urban,to take account of fire spread by radiation and firebrands in terms of statistical data, and to develop a computer program to perform the numerical simulation.

In this paper, we are concerned only with computer simulation of the fires of buildings ignited on urban areas produced by a nuclear burst. The numerical test is obtained sorne qualitative results for the simplest model by using the parameters of fire-spread from Japanese Hiroshima.