Journal Name:
- European Journal of Pure and Applied Mathematics
Author Name |
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Abstract (2. Language):
This paper presents an efficient approximate method to obtain a numerical solution,
which is bounded at the end point x = −1, for Cauchy type singular integral equations of
the first kind on the interval [−1,1]. The solution is derived by approximating the unknown
density function using the weighted Chebyshev polynomials of the third kind, and then computing
the Cauchy singular integral which is obtained analytically. The known force function
is interpolated using the Chebyshev polynomials of the fourth kind. The exactness of this
approximate method is shown for characteristic equation when the force function is a cubic.
Particular result is also given to show the exactness of this method.
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FULL TEXT (PDF):
- 3
462-472