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化学振荡研究领域的数学方法与程序软件*
- 褚效中;贺占博**
作者信息
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Mathematical Methods and Softwares in the Field of Chemical Oscillation
- Chu Xiaozhong;He Zhanbo**
Author information
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文章历史
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摘要
本文总结了已应用于化学振荡研究领域的数学方法和程序软件.其中在数学方法部分主要介绍了两种常用于求解化学振荡反应数学模型的吉尔(Gear)法和龙格-库塔(Runge-Kutta)法及其优缺点,并简要描述了3种研究化学振荡反应机理模型的数学分析方法--稳定性分析、灵敏度分析和主成分分析.同时结合作者的实践,给出了用两种功能强大的符号型数学运算软件--Mathematica和Maple来求解振荡反应数学模型的方法.文章还简要介绍了用来模拟化学振荡机理的遗传算法和蒙特卡罗(Monte Carlo)算法以及MECHEM和Chemical Kinetic Simulator(CKS)软件.
Abstract
The mathematical methods and computer softwares applied to the field of chemical oscillation are sum-marized in this paper. The main contents discussed are as follows: the advantages and disadvantages of Gear method and Runge-Kutta method in solving oscillation models; three mathematical analysis methods, i.e., stability analysis, sensi-tivity analysis and principal component analysis. Two powerful softwares, Mathematica and Maple are introduced accord-ing to the authors' practice. Additionally, two algorithms, genetic algorithm and Monte Carlo algorithm as well as two softwares MECHEM and Chemical Kinetic Simulator used in modeling mechanisms of chemical oscillations are also dealt with briefly.
关键词
化学振荡 / 数学方法 / 程序软件 {{custom_keyword}} /
Key words
chemical oscillation / mathematical method / program and software {{custom_keyword}} /
中图分类号：
O643.1
TP399
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参考文献
[ 1 ] Bray W C. J . Am. Chem. Soc. , 1921 , 43 :1262 —1268
[ 2 ] Tyson T. Belousov-Zhabotinsky Reaction. Berlin : Springer-Verlag , 1976
[ 3 ] Gear C W. Numeric Initial Value Problems in Ordinary Differential Equations. Englewood Cliffs : Prentice-Hall , 1971. 158 —166
[ 4 ] 徐洪义(Xu H Y) , 包雪松(Bao X S) , 王长富(Wang C F) . 计算数学(Mathematica Numerica Sinica) , 1985 , 7 (4) : 415 —419
[ 5 ] 李庆扬(Li Q Y) , 谢敬东(Xie J D) . 清华大学学报(自然科学版) (J . of Tsinghua University , NF) , 1991 , 31 (6) : 1 —11
[ 6 ] 谢敬东(Xie J D) . 硕士学位论文(Master Dissertation) , (Department of Applied Mathematics ,Tsinghua University) . 1990
[ 7 ] 徐士良(Xu S L) . FORTRAN 常用算法程序集(Book of Fortran Algorithm and Program) . 北京(Beijing) : 清华大学出版社(Tsinghua University Press) , 1995. 267 —274
[ 8 ] Kovács K M, Rábai G. J . Phys. Chem. A , 2001 , 105 (40) :9183 —9187
[ 9 ] Rábai G, Okazak N , Hanazaki I. J . Phys. Chem. A , 1999 , 103(36) : 7224 —7229
[10] Russell W, Ian C , Kevin B. Comput . Chem. Eng. , 2000 , 24(2) : 625 —630
[11] Voss D A , Khaliq A Q M. Comput . Chem. , 2001 , 25 ( 1) :101 —107
[12] Parimal P , Siddhartha D , Pinaki B. Indian J . Chem. Technol . ,2001 , 8 (4) : 307 —313
[13] Cox S M, Matthews P C. J . Computational Physics , 2002 , 176(2) : 430 —455
[14] Butcher J C , Jackiewic Z Z. Applied Numerical Mathematics ,1996 , 21 : 385 —415
[15] Kaps P , Rentrop P. Numer.Math. , 1979 , 33 : 55 —58
[16] 张韵华(Zhang Y H) , 奚梅成(Xi M C) , 陈长松(Chen C S) .数值计算方法和算法(Numeric Calculating Solution and Algorithm) . 北京(Beijing) : 科学出版社( Science Press) , 2000.153 —157
[17] Frerich G A , Thompson R C. J . Phys. Chem. A , 1998 , 102(42) : 8142 —8149
[18] Villadsen J , Michelsen M L. Solution of Differential Equation Models by Polynomial Approximation. Englewood Cliffs : Prentice Hall , 1978. 1
[19] Hindmarsh A C. Scientific Computing ( eds. Stepleman R S , et al . ) . Amsterdam: North-Holland , 1983. 559
[20] Petrascu A M, Michel HJ , Fórsterling H D. J . Phys. Chem. A ,1999 , 103 (34) : 6757 —6765
[21] 胡健伟(Hu J W) , 汤怀民(Tang H M) . 微分方程的数值解法(Numeric Solution in Ordinary Differential Equations) . 北京(Beijing) : 科学出版社(Science Press) , 1999
[22] 李庆扬(Li Q Y) , 王能超(Wang N C) , 易大义(Yi D Y) . 常微分方程的数值解法(第四版) ( Numerical Solution in Ordinary Differential Equations , Fourth Edition) . 北京(Beijing) : 清华大学出版社(Tsinghua University Press) , 2001
[23] 袁新鼎(Yuan XD) , 费景高(Fei J G) , 刘德贵(Liu D G) . 刚性常微分方程初值问题的数值解法(Numeric Initial Value Problems in Stiff Ordinary Differential Equations) . 北京(Beijing) : 科学出版社(Science Press) , 1978
[24] Akien R C. Stiff Calculation. New York : Oxford University Press ,1985
[25] 李如生(Li R S) . 非平衡态热力学与耗散结构( Thermodynamics of Non-equilibrium State and Dissipative Structure) . 北京(Beijing) : 清华大学出版社(Tsinghua University Press) ,1986.100 , 270
[26] 刘秉正(Liu B Z) . 非线性动力学与混沌基础(Nonlinear Dynamics and Chaos) . 长春(Changchun) : 东北师范大学出版社(Northeast Normal University Publisher) , 1994. 17 —52
[27] 谢应齐(Xie Y Q) , 曹杰(Cao J ) . 非线性动力学数学方法(Mathematical Solution in Nonlinear Dynamics) . 北京(Beijing) :气象出版社(Weather Publisher) , 2001. 21 —44
[28] 辛厚文(Xin H W) . 非线性化学(Nonlinear Chemistry) . 合肥(Hefei) : 中国科学技术出版社(Science and Technology Pub lisher of China) , 1999. 60 —70
[29] Skumanich R. Mol . Sci . &Chem. Res. , 1982 , 2 (4) : 79 —84
[30] 赵学庄(Zhao X Z) . 化学反应动力学原理( Principle in Dynamic of Chemical Reaction) . 北京(Beijing) : 高等教育出版社(Higher Education Press) , 1984. 192 —197
[31] Dodge M C , Hecht T A. Int . J . Chem. Kinet . , 1975 , 7 (1) :155 —163
[32] Hwang J T, Dougherty E P , Rabitz H. J . Chem. Phys. , 1978 ,69 (11) : 5180 —5191
[33] Dougherty E P , Rabitz H. Int . J . Chem. Kinet . ,1979 , 11 (12) :1237 —1248
[34] Gottwald B A , Wanner G. Computing , 1981 , 26 : 355 —359
[35] Gottwald B A , Wanner G. Simulation , 1982 , 37 (5) : 169 —173
[36] Valko P , Vajda S. Comput . & Chem. , 1984 , 8 (4) : 255 —271 and references therein
[37] Shen J I. J . Chem. Phys. , 1999 , 111 (16) : 7209 —7214
[38] 田瑾(Tian J ) , 项静恬(Xiang J T) , 李宝惠(Li B H) . 经济、环境等非线性系统的预测和调控( Forecast and Control in Nonlinear Systems of Economics , Environment etc. ) . 北京(Beijing) : 中国统计出版社(China Statistical Press) , 2001
[39] Boissonade J , De Kepper P. J . Phys. Chem. , 1980 , 84 (5) :501 —506
[40] Chevalier T, Schreiber I , Ross J . J . Phys. Chem. , 1993 , 97(26) : 6776 —6787
[41] Manevitch L I. Nonlinear Dynamics , 2001 , 25 (1 —3) : 95 —109
[42] Golat M, Flashner H. Nonlinear Dynamics , 2002 , 28 (1) : 29 —51
[43] Okino M S , Mavrovouniotis M L. Chem. Rev. , 1998 , 98 (2) :391 —408
[44] Brown N J , Guoping Li , Koszykowski L. Int . J . Chem. Kinet . ,1997 , 29 (6) :393 —414
[45] Ibison P. J . Phys. Chem. , 1992 , 96 (15) : 6321 —6325 and references therein
[46] Vajda S , Valko P , Turanyi T. Int . J . Chem. Kinet . , 1985 , 17(1) : 55 —82
[47] 张文修(Zhang W X) , 梁怡(Liang Y) . 遗传算法的数学基础(Mathematical Foundation of Genetic Algorithm) . 西安(Xi′an) :西安交通大学出版社(Xi′an Communication University Publisher) , 2000
[48] 刘勇(Liu Y) , 康立山(Kang L S) , 陈毓屏(Chen Y P) . 非数值并行方法———遗传算法(Nonnumeric Parallel Method ———Genetic Algorithm) . 北京(Beijing) : 科学出版社( Science Press) ,1998
[49] Tsuchiya M, Ross J . J . Phys. Chem. A , 2001 , 105 ( 16) :4052 —4058
[50] 徐钟济(Xu Z J ) . 蒙特卡罗方法(Monte-Carlo Method) . 上海(Shanghai) :上海科学技术出版社(Shanghai Science and Technology Press) , 1985
[51] 裴鹿成(Pei L C) , 王仲奇(Wang Z Q) . 蒙特卡罗方法(Monte-Carlo Method) . 北京(Beijing) : 海洋出版社(Ocean Press) ,1998. 3 —9
[52] 李如生(Li R S) . 非平衡态热力学与耗散结构( Thermodynamics of Non-equilibrium State and Dissipative Structure) . 北京(Beijing) :清华大学出版社(Tsinghua University Press) , 1986.344 —351
[53] 周鲁(Zhou L) , 陈敏(Chen M) , 贾均红(Jia J H) 等. 四川联合大学学报( 工程科学版) (J . of Sichuan Union University(Engineering Science Ed. ) ) ,1997 , 1 (3) : 33 —37
[54] Ziff R M, Gulari E , Barshad Y. Phys. Rev. Lett . , 1986 , 56 :2553 —2557
[55] Albano E V. J . Chem. Phys. , 1996 , 109 (17) : 7498 —7505
[56] Evans J W. Langmuir , 1991 , 7 (11) : 2514 —2519
[57] ZhdanovV P Z, Kasemo B. Surf . Sci . Rep. , 1994 , 20 (3) :111 —114
[58] Imbihl R , Erti G. Chem. Rev. , 1995 , 95 (3) : 697 —733
[59] Jansen A D J . J . Mol . Catal . A: Chemical , 1997 , 119 : 125 —134
[60] Nicolis G, Prigogine I. Self-Organization in Non-equilibrium Systems. New York : Oxford University Press , 1977
[61] Gardiner C W. Handbook of Stochastic Methods. Berlin : Spinger Verlag , 1985
[62] Allen M P , Tidesley D T. Computer Simulation of Liquids. Oxford , 1978
[63] Gorecki J , Kawczynski A L , Nowakowski B J . Phys. Chem. A ,1999 , 103 (17) : 3200 —3209
[64] Valdés-Pérez R E. MECHEM Demos , www. cs. cmu. edul-scidiscPmechem. html
[65] Zeigarnik A V , Valdés-Pérez R E. J . Comput . Chem. , 1998 ,19 : 741 —753
[66] Valdés-Pérez R E. Artificial Intelligence , 1995 , 74 (1) : 191 —201
[67] Valdés-Pérez R E. J . Comput . Chem. , 1993 , 14 :1454 —1459
[68] Valdés-Pérez R E. J . Comput . Chem. , 1994 , 34 :976 —983
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