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Kress smoothing transformation for weakly singular Fredholm integral equation of second kind

Mohamed Saeed Bawazir, Hassan (2006) Kress smoothing transformation for weakly singular Fredholm integral equation of second kind. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science.

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This work investigates a numerical method for the second kind Fredholm integral equation with weakly singular kernel k(x, y), in particular, when k(x, y) = ln |x-y|, and k(x, y) = |x-y|-a, -1 = x, y = 1, 0 < a < 1. The solutions of such equations may exhibit a singular behaviour in the neighbourhood of the endpoints x = ±1. We introduce a new smoothing transformation based on the Kress transformation for solving weakly singular Fredholm integral equations of the second kind, and then using the Hermite smoothing transformation as a standard. With the transformation an equation which is still weakly singular is obtained, but whose solution is smoother. The transformed equation is then solved numerically by product integration methods with interpolating polynomials. Two types of interpolating polynomials, namely the Gauss-Legendre and Chebyshev polynomials, have been used. Numerical examples are presented to investigate the performance of the former.

Item Type:Thesis (Masters)
Additional Information:Thesis (Master of Science (Mathematics)) - Universiti Teknologi Malaysia, 2006; Supervisor : Assoc. Prof. Dr. Ali bin Abd Rahman
Uncontrolled Keywords:numerical solution, Fredholm integral equation, Kress transformation, quadrature formula
Subjects:Q Science > QA Mathematics
ID Code:5302
Deposited By: Ms Zalinda Shuratman
Deposited On:07 Apr 2008 04:11
Last Modified:11 Jul 2012 01:27

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