反应工程中一类二阶常微分方程边值问题的初值化及求解  

Determination of Initial Values by Using Dichotomy and Solution for the Boundary Value Problems of a Class of Second Order Ordinary Differential Equations Arising in Reaction Engineering

作　　者：秦效英[1] 孙彦平[2] 

机构地区：[1]太原理工大学理学院,太原030024 [2]太原理工大学化学化工学院,太原030024

出　　处：《太原理工大学学报》2011年第1期92-95,共4页Journal of Taiyuan University of Technology

基　　金：国家自然科学基金资助项目(20776091)

摘　　要：对于在反应工程中常见的一类特殊的二阶常微分方程边值问题,给出了二分法初值化求解的一种新方法。具体求解了多孔催化剂和多孔电极两个数学模型,给出了在不同参数下二者解的曲线。与传统的打靶法相比,此方法回避了复杂的迭代运算,只需用简单的二分法求解一个变上限函数表达的初值满足的方程。此方法利用MATLAB计算广义积分精度高的特点所确定的初值也可以达到很高的精度。A new method for computing initial values for a class of special boundary value problems of second order ordinary differential equations arising from reaction engineering was given. Two mathematical models for porous catalyst and porous electrode were solved concretely and for different values of parameters the graphs of their solutions were depicted. Comparing with traditional shooting method this method avoided the complex iterative operation and only needed solving an equation satisfied by initial value which is expressed by a variable upper limit function. Based on the high precision of computing the generalized integral using MATLAB the initial values determined by this method are also of high precision.

关 键 词：二阶常微分方程 初边值问题 变上限函数 二分法 浓度分布 电势分布 

分 类 号：TQ035[化学工程]