求解奇异摄动转向点问题的一个高阶格式

§1.引言本文考虑以下奇异摄转向点问题: (1.1)这里参数ε是(0,1]中常数,函数α(x)∈C~2[I],b(x),f(x)∈C~3[I],且满足α(x)≥α_*>0,b(x)≥b_*>0,在以上假设下,由[2]可知,方程(1.1)存在唯一解u_ε∈C~4[I],且满足以下不等式     

平面混合流拟序结构的直接数值模拟

采用高阶精度差分格式,求解二维可压缩N-S方程,直接数值模拟了可压缩平面混合流的二维拟序结构.给出了流动失稳、Kelvin-Helmholtz不稳定波的发展、展向大涡的卷起和相邻两涡卷对并,包括3次对并的发展过程.研究了平面混合流时-空的发展和可压缩效应对其发展的影响.     

一类对流扩散方程的特征-修正差分格式及最大模估计

1 引 言许多物理问题的数学模型都可归结为对流扩散型方程（组）,这类模型具有较强的双曲性质.为了在数值计算中更好地反映这种性质,Douglas,Russell[1]提出了特征法的思想.特征法的主要特点是将模型方程的对流项隐含在解沿特征方向的导数之中,以沿特征方向的向后差商逼近取代了通常方法中沿时间方向的向后差商逼近.由于解在特征方向上的变     

THE UNCONDITIONAL CONVERGENT DIFFERENCE METHODS WITH INTRINSIC PARALLELISM FOR QUASILINEAR PARABOLIC SYSTEMS WITH TWO DIMENSIONS

In the present work we are going to solve the boundary value problem for the quasilinear parabolic systems of partial differential equations with two space dimensions by the finite difference method with intrinsic parallelism.Some fundamental behaviors of general finite difference schemes with intrinsic parallelism for the mentioned problems are studied.By the method of a priori estimation of the discrete solutions of the nonlinear difference systems,and the interpolation formulas of the various norms of the discrete functions and the fixed-point technique in finite dimensional Euclidean space,the existennce of the discrete vector solutions of the nonliear difference system with intrinsic parallelism are proved .Moreover the convergence of the discrete vector solutions of these difference schemes to the unique generalizd solution of the original quasilinear parabolic problem is proved.     

Small-scale ion flux and magnetic field fluctuations in solar wind, foreshock and magnetosheath

We have continued investigation of waves in the regions of undisturbed solar wind, foreshock and magnetosheath. The analysis of ion flux and magnetic field variations with the time interval 1-240s was performed in the regions above. Very large variation in such a time interval can be considered the common feature of the foreshock and magnetosheath. The results of case and statistical studies showed that the level of relative variations of ion flux and magnetic field magnitude in foreshock is about 3 times larger than in undisturbed solar wind. Variations of these parameters in the magnetosheath topologically connected with the quasi-parallel bow shock are about two times larger than those behind the quasi-perpendicular. We also compared the results from Interball-1 data analysis with those from statistical analysis of cluster magnetic field measurements. The magnetic field variations obtained from the different satellite data coincide with each other very well not only in quality but also in quantity.     

解线性抛物方程的一类新格式

解线性抛物方程的一类新格式孙志忠（中国科学院计算中心）ＡＮＥＷＣＬＡＳＳＯＦＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＳＦＯＲＬＩＮＥＡＲＰＡＲＡＢＯＬＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＳｕｎＺｈｉ－ｚｈｏｎｇ（ＣｏｍｐｕｔｉｎｇＣｅｎｔｅｒ，Ａ...     

解拟线性抛物方程的一类二阶差分格式

解拟线性抛物方程的一类二阶差分格式孙志忠（中国科学院计算中心）ＡＣＬＡＳＳＯＦＳＥＣＯＮＤ－ＯＲＤＥＲＡＣＣＵＲＡＴＥＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＳＦＯＲＱＵＡＳＩ－ＬＩＮＥＡＲＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＳ￥ＳｕｎＺｈｉ－ｚｈｏｎｇ（Ｃｏ...     

对流扩散方程的一类迎风格式

这里Ω为R~2中的有界区域,?Ω为其边界;a为正常数,c(x,y)和b(x,y)=(b_1(x,y),b_2(x,y))τ分别是?上的光滑函数和向量函数,且0相似文献   

两个恒稳定的差分格式

§1. 差分格式在节点(x_m,t_n)处,用u(x_m,t_n)表示微分方程的解,用u_m~n表示差分方程的解.1.跳点格式.由[1]的格式(5.10):