• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.867-872
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• 1999

In this paper we study the stability theorems for nonlinear Fredholm-Volterra integral equations system.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.223-236
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• 2000

In this paper, we solve the Fredholm integral equation of the first and second kind when the kernel takes a singular form. Also, some important relations for Chebyshev polynomial of integration are established.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권1호
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• pp.111-123
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• 2005

Here, the Fredholm integral equation with Hilbert kernel is solved numerically, using two different methods. Also the error, in each case, is estimated.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1995년도 추계학술대회 논문집
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• pp.664-667
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• 1995

The purpose of this paper is to consider the disk failure phenomenon based on the second kind Fredholm integral equation and numerical inversion of Laplace transform when the head hit disk asperities at HDI under antiplane impact loading. The model for analysis is a two layeered half-space with a circumferential surface edge crack. The optimum design parameters to reduce the disk failure due to impact are presented

• 대한수학회지
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• 제45권1호
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• pp.121-136
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• 2008

Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.165-182
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• 2003

Toeplitz matrix method and the product Nystrom method are described for mixed Fredholm-Volterra singular integral equation of the second kind with Carleman Kernel and logarithmic kernel. The results are compared with the exact solution of the integral equation. The error of each method is calculated.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.609-621
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• 2013

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.503-512
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• 1999

The purpose of this paper is to introduce the (Toeplitz) quadrature method for solving fredholm integral equations of the second kind with mildly singular kernels. We are presented some numerical examples for the computation of the error estimate using the MathCad package.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.261-275
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• 2002

Besides asymptotic method, the method of orthogonal polynomials has been used to obtain the solution of the Fredholm integral equation. The principal (singular) part of the kerne1 which corresponds to the selected domain of parameter variation is isolated. The unknown and known functions are expanded in a Chebyshev polynomial and an infinite a1gebraic system is obtained.

• Composites Research
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• 제15권4호
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• pp.37-42
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• 2002

면외전단하중(anti-plane shear loading)을 받는 기능경사 압전 세라믹 무한 스트립(functionally graded piezoelectric ceramic strip)의 상하 양쪽 끝단의 중앙에 평행하게 존재하는 유한한 크기의 균열(Griffith crack)에 대한 특이응력(singular stress)과 전기장(electric field)을 선형 압전 이론(theory of linear piezoelectricity)을 이용하여 결정한다. 푸리에 변환(Fourier transform)을 이용하여 복합적분 방정식을 구성하며, 이를 제2종 Fredholm 적분 방정식(Fredholm integral equation of the second kind) 으로 표현한다. 또한 응력세기계수(stress intensity factor)와 에너지 해방률(energy release rate)에 대한 수치 결과를 제시하였다.