• 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.

• 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

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.709-717
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• 2005

Integral equations occur naturally in many fields of mechanics and mathematical physics. We consider the Fredholm integral equation of the first kind.In this paper we are interested in integral equation of convolution type. We give approximate solution by Meyer wavelets

• 제어로봇시스템학회논문지
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• 제9권9호
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• pp.658-663
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• 2003

In deterministic design of feedback controllers for uncertain dynamic systems, the upper bound of the uncertainty is very important to guarantee the stability of the closed loop system. In this paper, we assume that the upper bound of the uncertainty is formulated using a Fredholm integral equation of the first kind, that is, an integral of the product of a predefined kernel with an unknown influence function. We propose an adaptation law that is capable of estimating this upper bound. Using this adaptive upper bound, we design an adaptive variable structure control (AVSC), which guarantees asymptotic stability/ultimate boundedness of uncertain dynamic systems. The illustrative example shows the proposed AVSC is effective for uncertain dynamic systems.

• 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.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.293-300
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• 1998

The numerical method is used to solve the Fredholm integral equation of the second kind with weak singular kernels using the Toeplitz matrices. The solution has a computing time requir-ment of O(N2) where 2N+1 is the number of discretization points used. Also the error estimate is computed. Some numerical Exam-ples are computed using the Mathcad package.

• 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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• 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.

• 한국해안해양공학회지
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• 제2권1호
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• pp.11-17
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• 1990

심해 파랑변형으로부터 형성된 Dirichlet 경계치 문제를 free space Green함수를 써서 경계적 분방정식으로 바꾸었으며 이 적분방정식을 Cubic spline 요소법을 사용하여 차분한 수치모델이 제시되었다. 유도된 제 1종 Fredholm적분방정식의 수치계산시 안정도를 높이기 위한 Hsiao와 MacCamy(1973) 방법이 사용되었다. 수치계산 결과의 검증을 위해 엄밀해가 존재하는 두 경우를 택하여 비교하였고, 본 모델의 높은 정밀도가 입증되었다.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.869-885
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• 2021

In this article, we define Picard's three-step iteration process for the approximation of fixed points of Zamfirescu operators in an arbitrary Banach space. We prove a convergence result for Zamfirescu operator using the proposed iteration process. Further, we prove that Picard's three-step iteration process is almost T-stable and converges faster than all the known and leading iteration processes. To support our results, we furnish an illustrative numerical example. Finally, we apply the proposed iteration process to approximate the solution of a mixed Volterra-Fredholm functional nonlinear integral equation.