Document Details
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Document Type |
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Thesis |
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Document Title |
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FINITE DIFFERENCE SCHEMES FOR NUMERICAL STUDY OF NON_LINEAR COUPLED REACTION DIFFUSION SYSTEM مخططات الفروق المحدودة لدراسة عددية لنظام رد فعل الانتشار المزدوج غير الخطي |
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Subject |
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Faculty of Sciences |
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Document Language |
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Arabic |
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Abstract |
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Some of the more widely used finite difference techniques for solving partial differential equations, are described in detailed, in this thesis. In particular to reaction diffusion system, in which one and two dimension coupling have been considered. Simple one and two dimensional Fisher Kolmogorov Petrovsky Piscounov (F-KPP) equations are also considered as special cases of the above mentioned system. Both explicit and implicit finite difference techniques are considered and compared on the basis of the computer capability and computational economy. Topics such as consistency of the finite difference equation with corresponding linear or non-linear partial differential equations, stability of the finite difference equations, and convergence of the solution of the finite difference equation to that of partial differential equations, are considered in detail. The accuracy of the different finite difference (FD) schemes, which depends on the discretisation error involved, is considered both theoretically and by means of illustrative numerical examples. The use of variable grid spacings is also considered, so that a finer grid can be used to give more detailed results in regions of interest. We substitute some of these schemes in one dimensional reaction diffusion equation (F-KPP) and enhance our knowledge to one dimensional coupling of such system. In the same way, two dimensional F-KPP is analysed. At the end we draw our results for two dimension coupling system of modified reaction diffusion (F-KPP) model. The outcome of this thesis is achieved in four papers. Two of them are accepted to publish soon and two of them are under review. They are as follows:
1. The papers, which are accepted and will publish soon:
• Numerical Study of one dimensional Fisher’s KPP equation with Finite Difference
Schemes. ” American Journal of Computational Mathematics (AJCM)”, Accepted Paper ID: 1100573, 10, Jan. 2017.
• Two dimensional non-linear reaction diffusion equation with time efficient scheme.
” American Journal of Computational Mathematics (AJCM)”, Accepted Paper ID: 1100583, 7, Feb. 2017.
2. The papers, which are under review:
• Numerical approximation to non-linear one dimensional coupled reaction diffusion system. ” Computational and Applied Mathematics”, Springer International Publishing AG. Under Review Paper, 26, Jan. 2017.
• A Two Dimensional Non-linear Reaction Diffusion Coupled Modified Fisher’s KPP System with Time Efficient Scheme. ” Numerical Methods for Partial Differential Equations”, John Wiley and Sons, Under Review Paper, 11, Jan. 2017. |
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Supervisor |
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Dr. Daoud Suleiman Mohammed Mashat |
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Thesis Type |
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Doctorate Thesis |
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Publishing Year |
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1439 AH
2017 AD |
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Added Date |
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Sunday, October 22, 2017 |
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Researchers
| شاهد حسنين | Hassanein, Shahad | Researcher | Doctorate | |
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