摘要
一维抛物型偏微分方程可以用精细积分方法精确求解．当精细积分中的矩阵指数函数用它的Ｐａｄé逼近格式来代替时，可以得到一系列由简到繁，精度由低到高的差分格式，因而便于根据实际计算的需要进行选取．Ｐａｄé逼近格式的求解主要包括矩阵运算和线性方程组的求解．利用Ｐａｄé逼近格式对应的方程组系数矩阵为带状矩阵的特点，把原来在整个区域上求解的问题转化为分区域求解，从而实现了Ｐａｄé逼近的并行算法．
Onedimensional partial parabolic equations can be solved by highprecision integration method. A series of finite difference schemes, which are from simple to complex in forms, and from low order to high in accuracy, can be obtained when the exponential matrix function is approximated via the Padé approximants. The solutions of the Padé approximants are mainly concerned in the calculation of matrix and linear equations. As the equations' coefficient matrix has the property of narrow band, the problem can be solved in the subdomain instead of the whole domain. A parallel algorithm based on these methods is presented and evaluated. A numerical example is given to show that the finite difference scheme via Padé approximations and its parallel computing are efficient.
出处
《上海交通大学学报》
EI
CAS
CSCD
北大核心
1998年第8期77-80,共4页
Journal of Shanghai Jiaotong University
关键词
抛物型偏微分方程
PADÉ逼近
并行算法
partial parabolic equations
Padé approximations
parallel computing
