• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.869-881
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• 2020

Most first kind integral equations are ill-posed, and obtaining their numerical solution often requires solving a linear system of algebraic equations of large condition number, which may be difficult or impossible. This article proposes a regularization-direct method to numerically solve first kind Fredholm integral equations. The vector forms of block-pulse functions and related properties are applied to formulate the direct method and reduce the integral equation to a linear system of algebraic equations. We include a regularization scheme to overcome the ill-posedness of integral equation and obtain a stable numerical solution. Some test problems are solved using the proposed regularization-direct method to illustrate its efficiency for solving first kind Fredholm integral equations.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.23-37
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• 2011

In this paper, we use a modified Tikhonov regularization method to solve the Fredholm integral equation of the first kind. Under the assumption that measured data are contaminated with deterministic errors, we give two error estimates. The convergence rates can be obtained under the suitable choices of regularization parameters and the number of measured points. Some numerical experiments show that the proposed method is effective and stable.

• 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 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

• 대한전기학회논문지:시스템및제어부문D
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• 제53권4호
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• pp.207-211
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• 2004

We consider a class of uncertain nonlinear systems containing the uncertainties without a priori information except that they are bounded. For such systems, we assume that the upper bound of the uncertainties is represented as a Fredholm integral equation of the first kind and we propose an adaptation law that is capable of estimating the upper bound. Using this adaptive upper bound, a continuous robust control which renders uncertain nonlinear systems uniformly ultimately bounded is designed.

• 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.

• Structural Engineering and Mechanics
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• 제6권4호
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• pp.457-466
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• 1998

The dynamic response of an elastic torsion shaft of revolution is analysed by the Line-Loaded Integral Equation Method (LLIEM). A "Dynamic Point Ring Couple" (DPRC) is used as a fictitious fundamental load and is distributed in an elastic space along the axis of the shaft outside the shaft occupation. According to the boundary condition, our problem is reduced to a 1-D Fredholm integral equation of the first kind, which is simpler for solving than that of a 2-D singular integral equation of the same kind obtanied by Boundary Element Method (BEM), for steady periodically varied loading. Numerical example of a shaft with quadratic generator under sinusoidal type of torque is given. Formulas for stresses and dangerous frequency are mentioned.

• 조명전기설비학회논문지
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• 제20권8호
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• pp.42-47
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• 2006

본 논문에서는 로봇의 동력학에 대한 정확한 지식을 요구하지 않는 로봇 머니퓰레이터를 위한 경계 추정기법을 가진 슬라이딩 모드 제어기를 제안한다. 경계 추정을 위해 로봇 동력학의 불확실한 비선형 요소들의 경계치를 제 1종의 Fredholm 적분식을 이용하여 표현하고, 슬라이딩 평면 함수값만을 이용한 적응 기법을 제안한다. 또한 로봇 동력학의 중요한 두가지 특성인 왜대칭성과 양정치성을 이용하여 로봇 시스템의 점근적 안정성을 증명한다.

• 대한전기학회논문지:시스템및제어부문D
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• 제52권7호
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• pp.418-423
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• 2003

In order to describe the upper bound of the uncertainties without any information of the structure, we assume that the upper bound is represented as a Fredholm integral equation of the first kind, that is, an integral of the product of a predefined kernel with an unknown influence function. Based on the improved Lyapunov function, we propose an adaptation law that is capable of estimating the upper bound and we design a sliding mode control, which controls effectively for uncertain dynamic systems.

• Nuclear Engineering and Technology
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• 제16권2호
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• pp.89-96
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• 1984

현재 서울대학교 원자핵공학과에서 제작중인 SNUT-79 토카막 장치에서의 고온 플라즈마의 구속을 위해서 순인장력 D형 곡선을 가진 토로이달 자장 코일을 수치 해석적 방법으로 설계하였다. 16개의 D형 토로이달 코일 뭉치는 플라즈마가 없는 경우 자장의 세기가 3T가 되도록 설계하였다. 토로이달 리플은 플라즈마영역에서 평균 토로이달 자장의 4%이하이다. 6개로 된 평형 코일의 위치와 전류 값을 Fredholm 제1종 적분 방정식을 선형 방정식으로 변환하여 얻었다. 평형 자장의 곡률도는 플라즈마 루프의 수직 수평 방향의 변위에 대한 안정화 조건을 만족시켰다.