区间精细算法与长效精细算法的对比研究  

Comparative Study on the Interval HPD and the Permanently Effective HPD

作　　者：刘晓梅[1] 周钢[2] 宋效林[2] 

机构地区：[1]上海交通大学机械与动力工程学院,上海200240 [2]上海交通大学数学系,上海200240

出　　处：《东华大学学报（自然科学版）》2007年第6期722-728,共7页Journal of Donghua University(Natural Science)

基　　金：国家自然科学基金项目(50376039);教育部科学技术研究重点项目(03068)

摘　　要：如何应用精细算法求解非齐次或非线性问题是计算力学中的热点问题,通常采用区间精细算法,但这一方法的精细传递矩阵与t步长的区间有关,计算量很大.能否设计出"一次计算,终生使用"的长效精细算法是一个倍受关注的问题,尤其是针对非线性的情况.以Burgers方程为模型设计出一种能解决二次非线性困难的长效精细算法.这类技巧不难推广至一般的二次非线性PDE(偏微分方程),且有广泛的应用,还建立了相应算法的基础理论与误差分析.两个算例表明,计算结果十分令人满意.It is a hot spot that how to develope a method of HPD （high precise direct） for solving nonlinear and nonhomogeneous problems in computational mechanics. HPD-the interval HPD has been devised, usually used, but the amount of calculation is very large/or the HPD transfer matrix is always associated with interval. Therefore, Whether to design the long acting HPD-＂execute once for ever useful＂ especially for nonlinear cases or not is worthwhile to discuss. For the model -- Burgers equation, a permanently effective HPD was designed which is generalized easily to solve the quadric nonlinear PDE, and the corresponding basic theory and the error analysis has been constructed. The results of two examples show that the method of permanently effective HPD is extremely satisfying.

关 键 词：区间精细算法 长效精细算法 二项精细算法 

分 类 号：O214.4[理学—概率论与数理统计] O342[理学—数学]