Abstract
In this paper, The differential transform method is extended to solve the Cauchy type singular integral equation of the first kind. Unbounded solution of the Cauchy type singular Integral equation is discussed. Numerical results are shown to illustrate the efficiency and accuracy of the present solution.
Highlights
Consider the Cauchy type singular integral equation(CSIE) of the form 1 g t 1 t x dt K x g t dt f x, -1
Chakrabarti and Berge [4] have proposed an approximate method to solve CSIE (1) using polynomial approximation of degree n and collocation points chosen to be the zeros of Chebyshev polynomial of the first kind for all cases
Eshkuvatov et al.[7] discussed approximate solution of CSIE (1) when K(x, t) = 0 for four cases. They used weighted Chebyshev polynomials of the first, second, third and fourth kinds. They showed that the numerical solution is identical with the exact solution when the force function is a polynomial of degree one
Summary
Where K(x, t) and f(x) are given real valued functions belonging to the Holder class and g(t) is to be determined, occurs in varieties of mixed boundary value problems of mathematical physics, isotropic elastic bodies involving cracks and other related problems [1,2,3]. Chakrabarti and Berge [4] have proposed an approximate method to solve CSIE (1) using polynomial approximation of degree n and collocation points chosen to be the zeros of Chebyshev polynomial of the first kind for all cases. They showed that the approximate method is exact when the force function f(t) is linear. Abdulkawi [6] discussed the numerical solution of CSIE (1) for tow cases, unbounded and bounded, He approximated the unknown function by weighted Chebyshev polynomials of the first and second kind, respectively, and used Lagrange-Chebyshev interpolation to approximate the regular kernel.
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