Adomian分解法在反应工程非线性数模求解中的应用

张兴芳; 孙彦平

您当前的位置：

首页 >

文章列表页 >

Adomian分解法在反应工程非线性数模求解中的应用

化工与环境工程 | 更新时间：2026-09-14

- Adomian分解法在反应工程非线性数模求解中的应用
- Application of Adomian Decomposition Method to the Solution of Nonlinear Mathematical Models in Reaction Engineering
- 中北大学学报（自然科学版） 2009年30卷第2期页码：147-152
- 作者机构：
  
  太原理工大学洁净化工研究所
- 作者简介：
- 基金信息：
  
  国家自然科学基金资助项目(20776091)
- DOI：
  中图分类号：
- 纸质出版：2009
- 稿件说明：
移动端阅览
张兴芳, 孙彦平. Adomian分解法在反应工程非线性数模求解中的应用[J]. 中北大学学报（自然科学版）, 2009,30(2):147-152.

张兴芳, 孙彦平. Application of Adomian Decomposition Method to the Solution of Nonlinear Mathematical Models in Reaction Engineering[J]. 2009, 30(2): 147-152.
张兴芳, 孙彦平. Adomian分解法在反应工程非线性数模求解中的应用[J]. 中北大学学报（自然科学版）, 2009,30(2):147-152. DOI：

张兴芳, 孙彦平. Application of Adomian Decomposition Method to the Solution of Nonlinear Mathematical Models in Reaction Engineering[J]. 2009, 30(2): 147-152. DOI：

摘要

针对传统数值求解方法存在的不足

将Adomian分解法(Adomian Decomposition Method

ADM)引入到反应工程非线性数模求解中

可给出非线性数模逼近解析解的代数表达式.介绍了ADM的基本原理及其近年来在反应工程非线性数模求解中的应用进展

给出了ADM求解多孔催化剂、多孔电极及填充床电极理论数模的实例

并对其求解多种反应工程数模的应用前景作了展望.实践证明:在求解精度和收敛速度方面

ADM是一种替代数值计算的有效方法.

Abstract

Aiming at the shortage of traditional numerical methods

the Adomian Decomposition Method(ADM) is introduced to solve the nonlinear model equations in reaction engineering.ADM can give the approximate analytical solutions in a form of algebraic expressions for nonlinear equations.The principle of ADM is introduced

and the recent progress of application of ADM to solving the nonlinear models in reaction engineering is reviewed.The solutions of theoretical models of porous catalysts

porous electrodes and packed bed electrodes are presented as examples.Furthermore

the application prospect of ADM to solving various systems of nonlinear equations in reaction engineering is outlined.Practice proves that ADM is an effective method to substitute numerical way in aspect of precision as well as convergence speed.

关键词

Keywords

references

Aris R.Mathematical Theory of Diffusion and Reaction in Permeable Catalyst[M].Oxford:Clarendon Press,1975.

Finlayson B A.Nonlinear Analysis in Chemical Engineering[M].New York:Mc Graw-Hill Inc,1980.

Newman J S.Electrochemical Systems.3rd Edition[M].New Jersey:Prentice Hall,2004.

Dieter B.Digital Simulation in Electrochemistry.4rd Edition[M].Springer:Brelin,2005.

Adomian G.The solution of general liner and nonlinear stochastic system[J].J.Rose Ed,1976(6):160-170.

Adomian G.Stochastic Operators and Dynamical System,Information Linkage Between Applied Mathematics andIndustry[M].Boston:Academic Press,1976.

方锦清.逆算符理论方法及其在非线性物理中的应用[J].物理学进展,1993,13(4):441-558.Fang Jinqing.Inverse operator theory method and its applications in nonlinear physics[J].Progress in Physics,1993,13(4):441-558.(in Chinese)

Adomian G.Solving Frontier Problem of Physics:the Decomposition Method[M].Boston:Kluwer,1994.

Adomian G,Rach R.Modified Adomian polynomials[J].Math.Comput.Model,1996,24(11):39-46.

武宝亭.一类强非线性偏微分方程组初边值问题之逆算符解法新探[J].数学物理学报,1999,19(3):347-355.Wu Baoting.A new exploration of the inverse operator solution for a kind of strong nonlinear partial differentialequations with initial-boundary value problems[J].Acta Mathematica Scientia,1999,19(3):347-355.(inChinese)

孙彦平,刘世斌,武宝亭,等.扩散-反应非线性数模逼近解析解[J].自然科学进展,2003,13(2):146-151.Sun Yanping,Liu Shibin,Wu Baoting,et al.Approximate solution for the nonlinear model of diffusion andreaction[J].Progress in Natural Science,2003,13(2):146-151.(in Chinese)

Sun Yanping,Liu Shibin,Scott Keith.Approximate solution for the nonlinear model of diffusion and reaction inporous catalysts by the decomposition method[J].Chemical Engineering Journal,2004,102:1-10.

Liu Shibin,Sun Yanping,Scott Keith.Analytic solution of diffusion reaction in spherical porous catalyst[J].Chem.Eng.Technol.,2003,26(1):87-95.

Scott K,Sun Y P.Approximate analytical solutions for models of three-dimensional electrodes by adomian’sdecomposition method[J].Modern Aspects of Electrochemistry,2007(41):221-304.

Sun Yanping,Scott K.An analysis of the influence of mass transfer on porous electrode performance[J].ChemicalEngineering Journal,2004,102:83-91.

Sun Yanping.The influence of mass transfer on a porous fuel cell electrode[J].Fuel Cell,2004,4(1-2):30-38

孙彦平.关于多孔电极理论数模及非线性分析[J].化工学报,2007,58(9):2161-2168.Sun Yanping.Modeling and non-linear analysis of porous electrodes[J].Journal of Chemical Industry andEngineering,2007,58(9):2161-2168.(in Chinese)

张兴芳.填充床电极反应器中典型有机电合成反应系统的选择性分析[J].化工学报,2008,59(5):1165-1170.Zhang Xingfang.Analysis of reaction selectivity of electro-organic synthesis system in packed bed electrode reaction[J].Journal of Chemical Industry and Engineering,2008,59(5):1165-1170.(in Chinese)

侯宝林.ADM机械化求解反应工程数模中非线性常微分方程边值问题[J].计算机与应用化学,2006,23(3):256-259.Hou Baolin.Applying ADM mechanization for solving nonlinear boundary value problem of ordinary differentialequation in reaction engineering[J].Computers and Applied Chemistry,2006,23(3):256-259.(in Chinese)

侯宝林,孙彦平.ADM机械化求解DLFFC多孔阳极理论数模[J].计算机与应用化学,2006,23(12):1250-1254.Hou Baolin,Sun Yanping.Appling ADM mechanization in solving theoretical models of porous anodes for DLFFC[J].Computers and Applied Chemistry,2006,23(12):1250-1254.(in Chinese)

浏览量

187

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

光纤环圈数控缠绕机主轴结构优化设计

具有非线性热源项耦合杆系统的整体吸引子

新型矿用逆变式快速充电电源的建模及仿真

模糊自适应PID在磁悬浮系统中的仿真研究

超高射频武器内弹道数值仿真