• Journal of applied mathematics & informatics
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• 제6권1호
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• pp.163-174
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• 1999

The purpose of this paper is to obtain the solution of Fredholm-Volterra integral equation with singular kernel in the space $L_2(-1, 1)\times C(0,T), 0 \leq t \leq T< \infty$, under certain conditions,. The numerical method is used to solve the Fredholm integral equation of the second kind with weak singular kernel using the Toeplitz matrices. Also the error estimate is computed and some numerical examples are computed using the MathCad package.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 추계학술대회논문집A
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• pp.341-348
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• 2001

A Mixed Volume and Boundary Integral Equation Method is applied for the effective analysis of plane elastostatic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions. It should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of anisotropic inclusions and voids or isotropic inclusions. Through the analysis of plane elastostatic problems in unbounded isotropic matrix with orthotropic inclusions and voids or isotropic inclusions, it will be established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions.

• 한국안전학회지
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• 제14권1호
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• pp.10-18
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• 1999

An integral equation representation of cracks was presented, which differs from well-known "dislocation layer" representation. In this new representation, the integral equation representation of cracks was developed and coupled to the direct boundary-element method for treatment of cracks in finite plane bodies. The method was developed for in-plane(mode I and II) loadings only. In this paper, the method is formulated and applied to various crack problems involving multiple and branch cracks in finite region. The results are compared to exact solutions where available and the method is shown to be very accurate despite of its simplicity.implicity.

• 대한기계학회논문집A
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• 제32권12호
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• pp.1072-1087
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• 2008

A mixed volume and boundary integral equation method (Mixed VIEM-BIEM) is used to calculate the plane elastostatic field in an isotropic elastic half-plane containing an isotropic or anisotropic inclusion and a void subject to remote loading parallel to the traction-free boundary. A detailed analysis of stress field at the interface between the isotropic matrix and the isotropic or orthotropic inclusion is carried out for different values of the distance between the center of the inclusion and the traction-free surface boundary in an isotropic elastic half-plane containing three different geometries of an isotropic or orthotropic inclusion and a void. The method is shown to be very accurate and effective for investigating the local stresses in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions and multiple voids.

• 대한전기학회논문지:전기물성ㆍ응용부문C
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• 제52권4호
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• pp.185-191
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• 2003

In this Paper, we propose an accurate and stable solution of the transient electromagnetic response from three-dimensional arbitrarily shaped conducting objects by using a time domain magnetic field integral equation. This method does not utilize the conventional marching-on in time (MOT) solution. Instead we solve the time domain integral equation by expressing the transient behavior of the induced current in terms of temporal expansion functions with decaying exponential functions and Laguerre·polynomials. Since these temporal expansion functions converge to zero as time progresses, the transient response of the induced current does not have a late time oscillation and converges to zero unconditionally. To show the validity of the proposed method, we solve a time domain magnetic field integral equation for three closed conducting objects and compare the results of Mie solution and the inverse discrete Fourier transform (IDFT) of the solution obtained in the frequency domain.

• 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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• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권2호
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• pp.67-80
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• 1998

In this paper the linear algebraic system obtained from a singular integral equation with variable coeffcients by a quadrature-collocation method is considered. We study this underdetermined system by means of the Moore Penrose generalized inverse. Convergence in compact subsets of [-1, 1] can be shown under some assumptions on the coeffcients of the equation.

• 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.

• 전산구조공학
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• 제10권2호
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• pp.213-223
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• 1997

탄성파의 변형 및 응력계산에 관한 연구는 비파괴검사를 비롯하여 광범위한 공학분야에서 중요한 역할을 하고 있다. 특히 파형의 산란문제가 많은 연구자들에 의해 다양한 방법으로 연구되고 있다. 실린더 또는 구와 같은 간단한 형상을 지닌 산란체에 대하여, 정상상태 탄성파의 산란문제의 해석은 해석적 기법을 이용한 연구가 가능하다. 하지만 임의의 형상을 갖는 산란체 또는 다수의 함유체에 대한 해석에는 수치해석방법이 요구된다. 예를 들면, 무한요소법 또는 Global-Local 유한요소법이라고 하는 혼성 유한요소법과 같은 특수한 유한요소법등이 개발되고 있다. 최근에는 경계요소법을 사용한 산란문제의 해석에 대한 연구가 진행되고 있다. 본 논문에서는 다수의 임의의 형상을 갖는 함유체, 공동 또는 크랙을 포함하고있는 무한고체에서의 일반적인 탄성동력학 문제를 해석하기 위해 새롭게 개발된 체적적분 방정식법을 소개한다. 또한 경계요소법을 사용하여 탄성파의 산란문제에 대한 수치해석을 수행하였으며, 이의 결과를 체적적분 방정식법의 결과와 비교 검토 하였다.