Date of Award

4-2019

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Advisor

Dr. Mohamed A. Hajji

Second Advisor

Dr. Youssef EL-Khatib

Third Advisor

Dr. Hishyar Khalil Abdullah

Comments

Wavelets has been a popular tool, since the late 1980s in many areas of engineering and mathematics. A major contribution of wavelets is their adaptation in the JPEG2000 picture format standard in 2000 and in the compression and storage of finger print scans. Since then wide applications of wavelets in different areas have emerged. Popular wavelets are the compactly-supported wavelets constructed by I. Daubechies. In this work, we use Daubechies’ wavelets to develop multistep algorithms for the solution of initial value problems (IVPs) in the context of Galerkin method. Though, such wavelet basis functions have good approximation property, they do not have explicit formulae, making finding inner products a challenge. This work tackles this point and uses the order of approximation of the wavelets to derive implicit multistep methods with comparable stability property to other methods. The derived methods are tested on linear and non-linear test equations.

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