Mathematics

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https://hdl.handle.net/20.500.11888/3206

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Browsing Mathematics by Author "Dr. Anwar Saleh"

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    Mathematical Theory of Wavelets
    (2009) Bothina Mohammad Hussein Gannam; Dr. Anwar Saleh
    Wavelets are functions that satisfy certain requirements and are used in representing and processing functions and signals, as well as, in compression of data and images, in many fields such as: mathematics, physics, computer science, engineering, and study of wavelet transform had been motivated by the need to the medicine. The overcome some weak points in representing functions and signals by the classical Fourier transform such as Gibbs phenomenon. In addition, wavelet transform have showed superiority over the classical Fourier transform. They converge faster than Fourier transform, leading to more efficient processing of signals and data. In this thesis, we overview the theory of wavelet transform, as well as, the theory of Fourier transform and make a comparative theoretical study between the tow major transforms proving the superiority of wavelet transform over the Fourier transforms in the speed of convergence and the accuracy or many functions
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    Multigrid Methods for Elliptic Partial Differential Equations
    (2010) Rania Taleb Mohammad Wannan; Dr. Anwar Saleh
    Partial differential equations appear in mathematical models that describe natural phenomena. Various methods can be used for solving such equations. In this thesis, an overview of classical iterative methods, as well as, the most recent multigrain methods is given. The classical iterative methods used are; the Jacobi, the Gauss-Seidel, and the SOR methods. Jacobi and Gauss-Seidel methods are efficient in smoothing the error but not in reducing it. The smoothing property of some classical methods motivated the work done on multigrain methods. Poisson's problem in one and two dimensions has been used as model problem in the study of multigrain methods. The study shows that the rate of convergence of multigrain methods does not depend on the mesh size, a feature that makes multigrain methods good accelerator of classical methods like Gauss-Seidel.