一阶常微分方程组的一个有效解法  

Effective solution method for the first-order ordinary differential equation system

作　　者：吕和祥[1] 董志强[1] 陈建峰[2] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024 [2]北京化工大学教育部超重力工程研究中心,北京100020

出　　处：《大连理工大学学报》2006年第5期629-632,共4页Journal of Dalian University of Technology

基　　金：辽宁省科学技术基金资助项目(20032116)

摘　　要：对于一阶常微分方程组,将具有导数变量的系数矩阵作三角化分解,使其简化成单位矩阵.应用具有三阶精度、单步自起步、无条件稳定的隐式算法对一阶常微分方程组进行了简化,改进了C a lahan算法.其中逆矩阵与矩阵的乘积,是通过矩阵三角化回代求解计算,从而回避了矩阵求逆.该算法保留了原方程组系数矩阵的稀疏存储方式和稀疏矩阵的运算规则,减少了计算时间和运算过程所需要的存储空间.For the first-order ordinary differential equation system, the coefficient matrix of variables with derivative is decomposed into the triangular factor form and transformed into unit matrix. The implicit numerical integration method with 3-order accuracy, single step and self-starting, and unconditional stablity is applied to reduce the first-order ordinary differential equation system. The algorithm improves Calahan＇s scheme. In this algorithm scheme, the multiplication of inverse matrix and a matrix is executed by the matrix triangular factor decomposition and back-substitution for the solution. The inverse matrix calculation is obviated. During operating the sparse matrix pattern of the original equation system and the rules of sparse matrix are reserved. So the storage spaces and the computation costs are reduced.

关 键 词：一阶常微分方程组 逐步积分 无条件稳定 瞬态温度场 

分 类 号：O241.4[理学—计算数学] O241.81[理学—数学]