计算机代数应用中的一个半逆序算法<sup>*</sup>

计算机代数应用中的一个半逆序算法^*

基金项目: * 国家自然科学基金;上海市自然科学基金;上海市高教局博士点基金

Shanghai Institute of Applied Mathematics and Mechanics, ShanghaiUniversity, Shanghai 200072, P. R. China

摘要: 为了克服计算机代数应用中出现的"中间表达式爆炸"的困难,本文提出一种半逆序算法,将中间表达式在运算过程中以符号形式冻结起来,到求解的最后阶段予以解冻,从而避免了因存贮空间不足而导致的溢出.文中简述了该算法在非线性振动、冷却塔动力优化和非线性水波问题中的应用,证实了算法的有效性.
- 计算机代数 /
- 符号运算 /
- 中间表达式爆炸 /
- 摄动法 /
- 非线性分析
Abstract: For the purpose of overcoming the difficulty of the so-called "intermediateexpression swell" in applying computer algebra, a semi-inverse algorithm is proposed.The order of seeking solutions for various problems is partly inverted, i. e., theintermediate expressions appearing in conrputation are frozen in the symbolic format first, and "unfrozen" till the formal expressions of final solulions are found out. Inthis way the overflow due to the shortage of saving space is avoided. The applicationsof the algorithm in the problems on nonllinear oscillation. dynamical optimization andinterfacial solilary waves are described. which show the effectiveness of the semi-inverse algorithm.
- computer algebra /
- symbolic computation /
- intermediate cxpression swell /
- perturbation method /
- nonlinear analysis

[1]	Crnllmei and J.A,Van Hulzen,Computer algebra algebra application,in Computer Algebra Symbolic and Allgebraic Computation,Ed,by B.Buchberger et al.,2nd Ed,,World Pub,Co.,Beijing(1988),245-258.
[2]	A,I,Beltzer Engineering analysis via symbolic computation-A break through Appl.Mech.Rev,,43 (1990),119-127.
[3]	M.Van Dyke,Compu:cr-axtended Seriles,Ann,Rev,Fluid Meeh.1(1984),287-309
[4]	H.R.Rand and D.Armbruster,Perturbation Methods,Bifurcation Theory and Computer Algebra,Springer-Yerlag,New York (1987).
[5]	减宏鸣,若干力学问题的摄动一计算机代数研究,硕士学位论文,上海工业大学.上海市应用数学和力学研究所(1993).
[6]	藏宏鸣,汁算机符号运算在摄动方法中的应用,上海工业大学学报,12 (1991),283-288.
[7]	减宏鸣、戴世强,一个非线性振动方程的计算机代数解,上海工业大学学报,1(1993),189-197.
[8]	戴世强,PLK方法,《奇异摄动理论及其在力学中的应用》,钱伟长主编,科学出版社,北京(1981),33-86.
[9]	Zang Hongming and Dai Shiqiang,Higher-order solutions for interfacial solitary waves in a two-fluid system,Proc,Inter,Conf.on Hydrodyn.,China Ocean Press.Beijing(1994),697-695
[10]	戴世强,两层流体界面上的孤立波,应用数学和力学,3(6) (1982),721-731.
[11]	王明琪、戴世强,一个非线性波动方程为计算机代数一摄动解,应用数学和力学,16(5) (1995),403-408.