关于非线性波动方程的爆破现象

通过引入一类“爆破因子K(u,ut）”,讨论了非线性波动方程分别具Newmann边界条件和Dirichlet边界条件时,混合问题对于常见的各种非线性情形及初值条件,解在有限时间内的爆破行为。     

不可微泛函拟极小问题解的正则性

本文对P＞1的情形给出不可微泛函I(u,G)= ∫FG（x,u, ↓△）dx的(1 cR^2u）一极小问题解梯度的Holder连续性证明。     

双光子光声效应理论

对双光子光声效应作了系统的理论分析，导出了双光子光声效应的波动方程，并求出双光子光声信号的表达式。 关键词：     

二维变系数扩散方程交替分组显格式的稳定性分析

1.引言 由于高性能并行计算机的出现和并行计算的推动,十多年来,抛物型方程有限差分并行算法设计与分析一直受到关注. D.J.Evalns和A.R.B.Abdullah(1983,[1,2]利用Saul’yev非对称格式对常系数抛物方程设计了AGE(交替分组显格式)算法,并用矩阵分析的方法证明了该算法的无条件稳定性.该算法有明显的并行性,倍受推崇,且计算的实践([8],[9])表明它对变系数的抛物方程也是可行的,但稳定性的分析成为一个难点.张宝琳([3])在一维情     

二维稳态各向异性介质渗透率的反演问题

1.引 言由多孔介质的渗流理论,二维稳态各向异性介质的渗流问题满足下列偏微分方程 -div(u(x,y)(?)u(x,y))=f(x,y),(x,y)∈Ω(?)R2, (1.1)     

不可压N-S方程的差分流线扩散法

In this paper, a Finite-Difference Streamline-Diffusion (FDSD as short) scheme for the incompressible Navier-Stokes Equations is constructed with linear finite element spaces. The analysis showes that the scheme considered has good stability and higher accuracy than the standard finite elemnet method.     

红黑排序混合算法收敛速度分析

The algorithm of applying the block Gauss elimination to the Red-Black or-dering matrix to reduce the order of the system then solve the reduced system byiterative methods is called Hybrid Red-Black Ordering algorithm.In this paper,we discuss the convergence rate of the hybrid methods combined with JACOBI,CG,GMRES(m).Theoretical analysis shows that without preconditioner thesethree hybrid methods converge about 2 times as fast as the corresponding natural ordering methods.For the case that all the eigenvalues is near the real axis, the GMRES(m) algorithm converges about 3 times faster than the natural ordering GMRES(m).Various numerical experiments are presented.For large scale prob-lem with preconditioners, numerical experiments show that the GMRES(m) hybrid methods converge from about 3 times to even 5 times as fast as the natural order-ing methods and the computing time is reduced to about 1/3 even 1/6 of that of the natural ordering methods.