摘要
一维扩散方程初边值问题可以用子城精细积分方法求解．子域积分可以采用不同数量的内点，单内点是最简单的情况．当单内点精细积分中的传递函数，即指数函数用其泰勒展开式的一阶近似来代替时，精细积分可转化为差分方程．文中对精细积分六点及多层格式的截断误差做了研究，提出了精细积分的六点加权格式和改进的多层格式，两种格式有较高精度，并且为无条件稳定．改进的多层格式还可以推广到多内点子域精细积分方法．
The initial problem of one-dimensional diffusion equations can be solved using global or sub-domain high precision direct integration method. One-point high precision direct integration method is the simplest case of this method. When the exponential function in this method is replaced by different expressions of its approximation, this method is transferred to different finite difference methods. The study about the truncation error of sixpoints and multilayer high precision direct integration methods is made in this paper. Two new methods, six-points weighted high precision direct integration method and improved multilayer method, are advanced. The two methods have higher precision and are unconditional stable. The improved multilayer method also can be extended to multipoints sub-domain high precision direct integration method.
出处
《上海交通大学学报》
EI
CAS
CSCD
北大核心
1996年第3期34-39,共6页
Journal of Shanghai Jiaotong University
基金
中国工程物理研究院
西安交通大学机械结构强度和振动国家重点实验室
国家教委留管司和优秀年轻教师基金
关键词
扩散方程
初边值问题
精细时程积分
截断误差
initial problem of diffusion equations
high precision direct integration method
truncation error
stability
