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A NUMERICAL ANALYSIS APPROACH FOR ESTIMATING THE MINIMUM TRAVELING WAVE SPEED FOR AN AUTOCATALYTIC REACTION

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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 auto-catalyst. 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 fourth-order Runge-Kutta 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, Yuan-wei , 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 auto-catalyst. 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 fourth-order Runge-Kutta method (RK4).
Identifier: CFE0002061 (IID), ucf:47571 (fedora)
Note(s): 2008-05-01
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

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