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Numerical Experiments on Eigenvalues of Weakly Singular Integral Equations Using Product Simpson's Rule

Razali, Mohamad Rashidi and Mohamed, M. S. Nasser (2002) Numerical Experiments on Eigenvalues of Weakly Singular Integral Equations Using Product Simpson's Rule. Matematika, 18 (1). pp. 9-20. ISSN 0127-8274

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Abstract

This paper discusses the use of Product Simpson’s rule to solve the integral equation eigenvalue problem f(x) = R 1−1 k(|x − y|)f(y)dy where k(t) = ln|t| or k(t) = t−, 0 < < 1, , f and are unknowns which we wish to obtain. The function f(y) in the integral above is replaced by an interpolating function Lfn(y) = Pni=0 f(xi)i(y), where i(y) are Simpson interpolating elements and x0, x1, . . . ,xn are the interpolating points and they are chosen to be the appropriate non-uniform mesh points in [−1, 1]. The product integration formula R 1−1 k(y)f(y)dy Pni=0 wif(xi) is used, where the weights wi are chosen such that the formula is exact when f(y) is replaced by Lf n(y) and k(y)as given above. The five eigenvalues with largest moduli of the two kernels K(x, y) = ln|x − y| and K(x, y) = |x − y|−, 0 < < 1 are given. Keywords eigenvalue, product integration, singular kernel, integral equation.

Item Type:Article
Uncontrolled Keywords:eigenvalue; product integration; singular kernel; integral equation
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:2435
Deposited By: Ms Suriawati Sahari
Deposited On:31 Jul 2007 08:37
Last Modified:06 Jan 2011 02:04

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