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Your search keyword '"Nik Long, N. M. A."' showing total 2 results
Start Over Author "Nik Long, N. M. A." Topic approximation theory
2 results on '"Nik Long, N. M. A."'

1. Numerical solution of FIE of the second kind with Cauchy kernel.

Author

Eshkuvatov, Z. K., Abdulkawi, M., and Nik Long, N. M. A.

Subjects
MATHEMATICAL functions, SINGULAR integrals, CHEBYSHEV polynomials, NUMERICAL solutions to integral equations, APPROXIMATION theory, NUMERICAL analysis, APPLIED mathematics
Abstract

In this paper, we present numerical method for solving the Fredholm Integral Equation of the second kind with Cauchy kernel. The weighted Chebyshev polynomials of the second kind are used to approximate the unknown function. Inconstant coefficients are approximated by Chebyshev polynomials of the first kind. Special type of regular integrals are computed analytically. Finally, numerical results show the exactness and accuracy of the numerical method presented. [ABSTRACT FROM AUTHOR]

Published
2012
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2. On the Semi-bounded Solution of Cauchy Type Singular Integral Equations of the First Kind.

Author

Abdulkawi, M., Eshkuvatov, Z. K., and Nik Long, N. M. A.

Subjects
*APPROXIMATION theory, *INTEGRAL equations, *FUNCTIONAL equations, *CHEBYSHEV polynomials, *FUNCTIONAL analysis, *DENSITY functionals, *NUMERICAL analysis, *MATHEMATICAL analysis, *MATHEMATICS
Abstract

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. [ABSTRACT FROM AUTHOR]

Published
2009

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