• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.299-318
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• 2023

This article devises an exponentially fitted method for the numerical solution of two parameter singularly perturbed parabolic boundary value problems. The proposed scheme is able to resolve the two lateral boundary layers of the solution. Error estimates show that the constructed scheme is parameter-uniformly convergent with a quadratic numerical rate of convergence. Some numerical test examples are taken from recently published articles to confirm the theoretical results and demonstrate a good performance of the current scheme.

• Structural Engineering and Mechanics
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• v.16 no.3
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• pp.259-274
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• 2003

In this paper, a novel numerical solution technique, the differential cubature method is employed to study the buckling problems of thick plates with arbitrary quadrilateral planforms and non-uniform boundary constraints based on the first order shear deformation theory. By using this method, the governing differential equations at each discrete point are transformed into sets of linear homogeneous algebraic equations. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Detailed formulation and implementation of this method are presented. The buckling parameters are calculated through solving a standard eigenvalue problem by subspace iterative method. Convergence and comparison studies are carried out to verify the reliability and accuracy of the numerical solutions. The applicability, efficiency, and simplicity of the present method are demonstrated through solving several sample plate buckling problems with various mixed boundary constraints. It is shown that the differential cubature method yields comparable numerical solutions with 2.77-times less degrees of freedom than the differential quadrature element method and 2-times less degrees of freedom than the energy method. Due to the lack of published solutions for buckling of thick rectangular plates with mixed edge conditions, the present solutions may serve as benchmark values for further studies in the future.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.277-302
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• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.5
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• pp.407-419
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• 2008

In this study, the transition Reynolds number of compressible axi-symmetric sharp cone boundary layer is predicted by using a linear stability theory and the -method. The compressible linear stability equation for sharp cone boundary layer was derived from the governing equations on the body-intrinsic axi-symmetric coordinate system. The numerical analysis code for the stability equation was developed based on a second-order accurate finite-difference method. Stability characteristics and amplification rate of two-dimensional second mode disturbance for the sharp cone boundary layer were calculated from the analysis code and the numerical code was validated by comparing the results with experimental data. Transition prediction was performed by application of the -method with N=10. From comparison with wind tunnel experiments and flight tests data, capability of the transition prediction of this study is confirmed for the sharp cone boundary layers which have an edge Mach number between 4 and 8. In addition, effect of wall cooling on the stability of disturbance in the boundary layer and transition position is investigated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.392-398
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• 1998

In order to check the validity of nonlinear normal modes of continuous, systems by means of the energy-based formulation, we consider a beam with a nonlinear boundary condition. The initial and boundary e c6nsl of a linear partial differential equation and a nonlinear boundary condition is reduced to a linear boundary value problem consisting of an 8th order ordinary differential equations and linear boundary conditions. After obtaining the asymptotic solution corresponding to each normal mode, we compare this with numerical results by the finite element method.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1998.04a
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• pp.256-262
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• 1998

Many lubricated systems experience boundary, lubrication condition during operation. However, the friction and wear characteristics of boundary lubrication are not clearly understood. In this work the factors which affect the friction and wear between boundary lubricated metallic surfaces are investigated. Experiments were performed on atuminium, copper, and SM45C with bearing ball using a pin-on disk type tester. The experimental conditions were determined by Taguchi experimental method. From the experimental results, the major factors that influence the friction and wear characteristics of boundary lubrication could be identified.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.531-551
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• 2021

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing p(x)-Laplacian. More precisely, we consider the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.

• Journal of Electrical Engineering and Technology
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• v.11 no.6
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• pp.1571-1581
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• 2016

A novel method is proposed to construct the voltage stability boundary of power system considering different Reactive Power Control Mode (RPCM) of Doubly-Fed Induction Generator (DFIG) Wind Power Plant (WPP). It can be used for reflecting the static stability status of grid operation with wind power penetration. The analytical derivation work of boundary search method can expound the mechanism and parameters relationship of different WPP RPCMs. In order to improve the load margin and find a practical method to assess the voltage security of power system, the approximate method of constructing voltage stability boundary and the critical points search algorithms under different RPCMs of DFIG WPP are explored, which can provide direct and effective reference data for operators.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.651-665
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• 2017

Some computational fluid dynamics problems concerning the thin films flow of viscous fluid with a free surface and draining or coating fluid-flow problems can be delineated by third-order ordinary differential equations. In this paper, the aim is to introduce the numerical solutions of the boundary value problems of such equations by variational iteration method. In this paper, it is shown that the third-order boundary value problems can be written as a system of integral equations, which can be solved by using the variational iteration method. These solutions are gleaned in terms of convergent series. Numerical examples are given to depict the method and their convergence.

• Smart Structures and Systems
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• v.22 no.5
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• pp.621-630
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• 2018

Boundary effect and the noise robustness are the two crucial aspects which affect the effectiveness of the damage localization based on the mode shape measurements. To overcome the boundary effect problem and enhance the noise robustness in damage detection, a simple damage localization method is proposed based on the Singular Value Decomposition (SVD) for the mode shape of composite plates. In the proposed method, the boundary effect problem is addressed by the decomposition and reconstruction of mode shape, and the noise robustness in enhanced by the noise filtering during the decomposition and reconstruction process. Numerical validations are performed on plate-like structures for various damage and boundary scenarios. Validations show that the proposed method is accurate and effective in the damage detection for the two-dimensional structures.