• Journal of applied mathematics & informatics
• /
• 제9권1호
• /
• pp.261-275
• /
• 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
• /
• 제4권2호
• /
• pp.85-97
• /
• 2000

A quadrature rule for the solution of Cauchy singular integral equation is constructed and investigated. This method to calculate numerically singular integrals uses classical Jacobi quadratures adopting Hunter's method. The proposed method is convergent under a reasonable assumption on the smoothness of the solution.

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

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

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

• 대한기계학회논문집A
• /
• 제20권4호
• /
• pp.1186-1193
• /
• 1996

The analytic solution of the stress field at creep crack in the presence of grain boundary caviation is to be obtained by solving the governing equation which was derived through the previous paper. The complex integral technique is used to slove the singular integral equation. under the help of the information about stress behaviors at the ends of integral region know by numerical solution. The resultant stress disstribution obtained shows the relaxed crack-tip singularity of $r^{1/2+\theta}$ due to the intervention of cavitation effect, otherwise, it should assumed to be $r^{1/2}$ singularity of linear elastic fracture mechanics with no cavitation.

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

• 충청수학회지
• /
• 제27권4호
• /
• pp.763-769
• /
• 2014

In this paper, we illustrate a counter example for the converse of a certain conjecture proposed by De Giorgi. De Giorgi suggested a series of conjectures, in which a certain integral condition for singularity or degeneracy of an elliptic operator is satisfied, the solutions are continuous. We construct some singular elliptic operators and solutions such that the integral condition does not hold, but the solutions are continuous.

• Journal of applied mathematics & informatics
• /
• 제31권5_6호
• /
• pp.877-894
• /
• 2013

In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green's function, a nonlinear alternative of Leray-Schauder type, Guo-Krasnoselskii's fixed point theorem in a cone. Some examples are included to show the applicability of our results.

• Structural Engineering and Mechanics
• /
• 제83권1호
• /
• pp.67-77
• /
• 2022

In this study, frictionless continuous and discontinuous contact problems of a magneto-electro-elastic layer in the presence of the body force were discussed. The layer was indented by a rigid cylindrical insulating punch and supported by a rigid substrate without bond. Applying the Fourier integral transform technique, the general expressions of the problem were derived in the presence of body force. Thanks to the boundary conditions, the singular integral equations were obtained for both the continuous and the discontinuous contact cases. Gauss-Chebyshev integration formulas were used to transform the singular integral equations into a set of nonlinear equations. Contact width under the punch, initial separation distance, critical load, separation regions and contact stress under the punch and between the layer, and substrate were given as a result.

• 대한기계학회논문집
• /
• 제10권5호
• /
• pp.787-797
• /
• 1986

본 논문에서는 축대칭 선형 문제의 경계적분법에 대한 일반화한 정식화 과정 및 수치적 접근방법이 제시되었으며 정식화 과정 중 Navier 방정식의 기본해로부터 도 출되는 변위 및 표면적 Kernel을 구하는 Hankel 변환법을 이용한 $\ulcorner$직접축대칭접근법 $\lrcorner$과 3차원 Kevin 해로부터 원주경로 따라 적분한 $\ulcorner$3차원 접근법$\lrcorner$이 비교 검토되었 다.