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On The Numerical Solution Of Reaction-diffusion System With Fast Reversible Reaction  


Abstract Category: Science
Course / Degree: M.Sc. in Mathematics, College of Computer Sciences and Mathematics, University of Mosul
Institution / University: University of Mosul, Iraq
Published in: 2013


Thesis Abstract / Summary:

In this thesis, we obtain the numerical solution of reaction-diffusion system with the reversible reaction by using two numerical methods, which are consistent and lumped finite element schemes, and some numeric-analytic methods which are Adomian decomposition method (ADM), variational iteration method (VIM), variational iteration method with an optimal auxiliary parameter (VIMOAP), variational iteration method using Adomian’s polynomials (VIMAP) and variational iteration method using Adomian’s polynomials with an optimal auxiliary parameter (VIMAPOAP) where the last one is a proposed technique to solve nonlinear problems as a new modification of VIMAP. A Practical application is provided for the fast reversible chemical reaction . The numerical results obtained by those methods are compared with each other to reveal that the numeric-analytic methods are more accurate and less computational workload compared with consistent and lumped finite element schemes but it converge slowly for large solution domains.

Also, the numerical stability analysis of the consistent and lumped finite element schemes is performed by using Fourier (Von Neumann) method to insure the stability of the obtained solutions. The analysis show that the consistent and lumped finite element schemes are unconditionally stable when while the consistent finite element method is stable if and when . Also, the lumped finite element method is stable if and when . At last, we study the effect of the chemical kinetics factor on the numerical solution behavior of the problem.


Thesis Keywords/Search Tags:
reaction-diffusion system; reversible reaction; Adomian decomposition method; variational iteration method; Adomian’s polynomials; finite element schemes; stability analysis

This Thesis Abstract may be cited as follows:
M.O. Al-Amr, M.Sc. Thesis, University of Mosul, 2013 (in Arabic).

Thesis Images:
Science - On The Numerical Solution Of  Reaction-diffusion System With Fast Reversible Reaction Mohammed O. Al-Amr
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Submission Details: Thesis Abstract submitted by Mohammed O. Al-Amr from Iraq on 27-Feb-2014 12:58.
Abstract has been viewed 2206 times (since 7 Mar 2010).

Mohammed O. Al-Amr Contact Details: Email: malamroo@yahoo.com



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