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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Abstract
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 xy, and k(x, y) = xya, 1 = x, y = 1, 0 < a < 1. The solutions of such equations may exhibit a singular behaviour in the neighbourhood of the endpoints x = Â±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 GaussLegendre 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 
Divisions:  Science 
ID Code:  5302 
Deposited By:  Ms Zalinda Shuratman 
Deposited On:  07 Apr 2008 04:11 
Last Modified:  17 Sep 2017 04:16 
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