Computational Mathmatics

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https://hdl.handle.net/20.500.11888/3205

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Browsing Computational Mathmatics by Author "Dr. Anwar Saleh"

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    Data Compression with Wavelets
    (2009) Rana Bassam Da'od Ismirate; Dr. Anwar Saleh
    There are two types of data compression; the first is lossless(exact) and the second is lossy (approximate). In lossless compression, all details are reserved but high compression ratios can not be achieved and this type is not considered in this thesis. The other type is the loss compression where some details are lost in the process of compression. The size of the lost details is proportional with the the desired compression ratio which is controlled by the user. Using this type, high compression ratios can be achieved with acceptable resolution in the reconstructed data. In this thesis, a computational study of the classical Fourier transform and the relatively new wavelet transform is done. In addition, a computational comparison between the two major transforms shows that the wavelet transform is more efficient than the classical Fourier transform. The high compression ratios that can be achieved by wavelet transform lead to the introduction of several wavelet-based lossy data compression software. Examples of these are the image compressor JPEG2000 and the text compressor DJVU.
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    Wavelets Numerical Methods for Solving Differential Equations
    (2015) Yousef Mustafa Yousef Ahmed Bsharat; Dr. Anwar Saleh
    In this thesis, a computational study of the relatively new numerical methods of Haar wavelets for solving linear differential equations is used. A comparison between the new method and some classical methods for linear differential equations has been made. The aim is to show the efficiency of the presented method and its advantage over other method. The new method is simple and its numerical results are close or more accurate than some classical methods