Document Details
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Document Type |
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Thesis |
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Document Title |
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Numerical Methods for Solving Fractional Differential Equation لطرق العددية لحل المعادلات التفاضلية ذات الرتب الكسرية |
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Subject |
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Faculty of Sciences > mathematics department |
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Document Language |
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Arabic |
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Abstract |
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Spectral methods are developed and implemented to solve some fractional differential equations (FDEs) which are modeling for some important real world problems. In all the used spectral methods, we should express the solution of the FDE by means of a truncated series of smooth global functions (such as the well Known orthogonal polynomials e.g. Legendre, Chebychev or Jacobi).
In deed, we develop the spectral collocation method in combination with operational matrices of some orthogonal polynomials, because of its versatility and simplicity, to solve linear and non-linear FDEs. One of the advantages of this method is that the FDE will be reduces to a system of algebraic equations which can be solved by many iterative methods. This provides an accurate approximation for a smooth solution with relatively few degree of freedom.
The outcome of this thesis is written in four papers (three of them are already published) their details are as follows:
A new numerical technique for solving fractional sub-diffusion and reaction sub-diffusion equations with a nonlinear source term, A. H. Bhrawy, D. Baleanu, F.Mallawi, Thermal Sciences, 19, 25-34 (2015).
An accurate Chebyshev pseudospectral scheme for multi-dimensional parabolic problems with time delays, A.H. Bhrawy, M.A. Abdelkawy, F. Mallawi,
Boundary Value Problems, 2015 (1), 1-20 (2015).
Application of Legendre Collocation method to space-time variable fractional-order advection-dispersion equation, A.H. Bhrawy, F. Mallawi, M.A. Zaky,
In process of publishing.
New Spectral Collocation Algorithms for One- and Two-Dimensional Schro ̈dinger Equations with Kerr Law Nonlinearity |
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Supervisor |
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Prof. Abdulrahman Saleh Al-Fhaid |
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Thesis Type |
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Doctorate Thesis |
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Publishing Year |
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1437 AH
2016 AD |
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Co-Supervisor |
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Dr. Ali Hassan Bhrawy |
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Added Date |
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Sunday, October 9, 2016 |
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Researchers
| فؤاد عثمان ملاوي | Mallawi, Fouad Othman | Researcher | Doctorate | |
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