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求解扩散方程的交替分段显-隐式方法

张宝琳   

  1. 北京应用物理与计算数学研究所;
  • 出版日期:1991-04-20 发布日期:1991-04-20

张宝琳. 求解扩散方程的交替分段显-隐式方法[J]. 数值计算与计算机应用, 1991, 12(4): 245-253.

AN ALTERNATING SEGMENT EXPLICIT-IMPLICIT METHOD FOR THE DIFFUSION EQUATION

  1. Zhang Bao-lin (Institute of Applied Physics and Computational Mathematics,Beijing)
  • Online:1991-04-20 Published:1991-04-20
本文的目的是研究适合在并行机与向量机上求解下述扩散方程的有限差分方法:求满足的解 u(x,t),适合初始条件 u(x,O)=f(x),O≤x≤l (2) 及边界条件 u(0,i)=g_0(t), u(1,t)=g_t(t). (3) 习知,在求解上述问题的有限差分逼近方法中,古典显式方法适合于并行计算,但不绝对稳定、而像古典隐式和Crank-Nicolson格式这类隐式方法是绝对稳定的,但需要求解线性代数方程组,实现并行计算有一定困难。D.J.Evans和 A.R.Abdullah 巧
The segment implicit scheme of finite difference approximation is constructed with the aid of Saulyev asymmetric schemes. Then a new alternating segment explicit-implicit method for the diffusion equation is developed, which is suitable for the computation on parallel and vector computers. The method is unconditionally stable and also gives more accurate solutions because of its better truncation error. In the numerical experiments for an example the accuracy of the method is compared with that of the AGE method (Evans and Abdullah).
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