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A NUMERICAL ANALYSIS APPROACH FOR ESTIMATING THE MINIMUM TRAVELING WAVE SPEED FOR AN AUTOCATALYTIC REACTION
 Date Issued:
 2008
 Abstract/Description:
 This thesis studies the traveling wavefront created by the autocatalytic cubic chemical reaction A + 2B → 3B involving two chemical species A and B, where A is the reactant and B is the autocatalyst. The diffusion coefficients for A and B are given by and . These coefficients differ as a result of the chemical species having different size and/or weight. Theoretical results show there exist bounds, and , depending on , where for speeds , a traveling wave solution exists, while for speeds , a solution does not exist. Moreover, if , and are similar to one another and in the order of when it is small. On the other hand, when there exists a minimum speed vmin, such that there is a traveling wave solution if the speed v > vmin. The determination of vmin is very important in determining the dynamics of general solutions. To fill in the gap of the theoretical study, we use numerical methods to determine vmin for various cases. The numerical algorithm used is the fourthorder RungeKutta method (RK4).
Title:  A NUMERICAL ANALYSIS APPROACH FOR ESTIMATING THE MINIMUM TRAVELING WAVE SPEED FOR AN AUTOCATALYTIC REACTION . 
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Name(s): 
Blanken, Erika, Author Qi, Yuanwei , Committee Chair University of Central Florida, Degree Grantor 

Type of Resource:  text  
Date Issued:  2008  
Publisher:  University of Central Florida  
Language(s):  English  
Abstract/Description:  This thesis studies the traveling wavefront created by the autocatalytic cubic chemical reaction A + 2B → 3B involving two chemical species A and B, where A is the reactant and B is the autocatalyst. The diffusion coefficients for A and B are given by and . These coefficients differ as a result of the chemical species having different size and/or weight. Theoretical results show there exist bounds, and , depending on , where for speeds , a traveling wave solution exists, while for speeds , a solution does not exist. Moreover, if , and are similar to one another and in the order of when it is small. On the other hand, when there exists a minimum speed vmin, such that there is a traveling wave solution if the speed v > vmin. The determination of vmin is very important in determining the dynamics of general solutions. To fill in the gap of the theoretical study, we use numerical methods to determine vmin for various cases. The numerical algorithm used is the fourthorder RungeKutta method (RK4).  
Identifier:  CFE0002061 (IID), ucf:47571 (fedora)  
Note(s): 
20080501 M.S. Sciences, Department of Mathematics Masters This record was generated from author submitted information. 

Subject(s): 
traveling wave autocatalytic cubic reaction partial differential equations 

Persistent Link to This Record:  http://purl.flvc.org/ucf/fd/CFE0002061  
Restrictions on Access:  public  
Host Institution:  UCF 