Numerical treatment of solving singular integral equations by using Sinc approximations |
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Authors: | Mohamed S Akel Hussein S Hussein |
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Institution: | Dept. of Math., Faculty of Science, King Faisal University, Al-Ahsaa 31982, P.O. Box 380, Saudi Arabia |
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Abstract: | In this paper we propose numerical treatment for singular integral equations. The methods are developed by means of the Sinc approximation with smoothing transformations. Such approximation is an effective technique against the singularities of the equations, and achieves exponential convergence. Therefore the methods improve conventional results where only polynomial convergence have been reported. The resulting algebraic system is solved by least squares approximation and leap frog algorithm. Estimation of errors of the approximate solution is presented. Some experimental tests are presented to show the efficient of the proposed methods. |
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Keywords: | Cauchy singular integral equations Regularization from the left Sinc approximation Smooth transformation Leap frog algorithm |
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