• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.845-858
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• 2021

We present new bounds for the numerical radius of bounded linear operators and 2 × 2 operator matrices. We apply upper bounds for the numerical radius to the Frobenius companion matrix of a complex monic polynomial to obtain new estimations for the zeros of that polynomial. We also show with numerical examples that our new estimations improve on the existing estimations.

• Structural Engineering and Mechanics
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• v.18 no.1
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• pp.59-78
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• 2004

This paper is devoted to illustrate some numerical procedures to solve the boundary equilibrium problems of three-dimensional solids that are subjected to thermal strains. The constitutive equations take into account the bounded tensile strength of the material and they are presented in the framework of non-linear elasticity and small strains. The associated equilibrium problem is solved numerically by means of the finite element method and the numerical techniques, i.e. the Newton-Raphson method and the secant method, are revised in order to assure the solution convergence of the discretized problem. Some numerical examples are illustrated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.401-406
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• 2002

A numerical model is introduced to simulate propagation, reflection, and scattering of elastic waves in solids. The model consists of mass points and linear springs, interconnected with in a lattice structure; hence, its name, the mass-spring lattice model (MSLM). The MSLM has successfully been applied to the numerical simulation and visualization of various elastic wave phenomena involved in ultrasonic nondestructive testing (NDT). This method is useful to simulate, design, or analyze actual testing. Some representative examples of numerical simulation using the MSLM are presented, and future work necessary for its further development Is addressed.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.383-393
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• 2021

In this paper, numerical techniques are presented for solving initial value problems of fractional differential equations with variable coefficients. The method is derived by applying a Taylor vector approximation. Moreover, the operational matrix of fractional integration of a Taylor vector is provided in order to transform the continuous equations into a system of algebraic equations. Furthermore, numerical examples demonstrate that this method is applicable and accurate.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.253-260
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• 2002

In this paper, a good interpolation formulae are applied to the numerical solution of Cauchy integral equations of the first kind with using some Chebyshev quadrature rules. To demonstrate the effectiveness of the Radau-Chebyshev with respect to the olds, [6],[7],[8] and [121, some examples are given.

• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.9-14
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• 2001

Astrophysics has been one of the disciplines which utilize actively supercomputers for their researches. In this paper, studies of astrophysical flows by large scale numerical simulations in supercomputers are discussed. The followings are described: 1) characteristics of astrophysical flows, 2) numerical codes to study astrophysical flows, 3) performance of the codes in parallel supercomputers. A couple of examples of such studies are briefly presented: 1) three-dimensional evolution of the nonlinear Kelvin-Helmholtz instability in a magnetized medium, 2) three-dimensional simulations of astrophysical jets in a magnetized medium.

• 한국전산유체공학회:학술대회논문집
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• 1997.10a
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• pp.10-15
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• 1997

Unsteady natural convection of an enclosed fluid has been one of the fundamental thermo-fluid problems, of which dynamic relevance is found in many engineering applications. Together with the inherent coupling between the boundary layers and the interior core, and strong interaction between flow and temperature fields, the unsteadiness poses serious hurdles for analytical and experimental approaches. With the recent development of computers and solution algorithms, computational fluid dynamics has become the prevailing tool to tackle the underlying problems. In this presentation, a few examples of numerical studies are introduced. The usefulness and potential of numerical simulations in investigating unsteady natural convection are elaborated.

• The Pure and Applied Mathematics
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• v.27 no.1
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• pp.35-42
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• 2020

In this paper, numerical algorithms for solving a fuzzy system of linear equations with crisp coefficients are presented. We illustrate the efficiency and accuracy of the proposed methods by solving some numerical examples. We also provide a graphical representation of the fuzzy solutions in three-dimension as a visual reference of the solution of the fuzzy system.

• Journal of KSNVE
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• v.4 no.4
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• pp.451-457
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• 1994

A numerical method is presented to obtain natural frequencies and mode shapes of uniform elastic beams with static deflections due to dead loads. The differential equation governing the free vibration of beam taken into account the static deflection due to deal loads is derived and solved numerically. The hinged-hinged, clamped-clamped and clamped-hinged end constraints are applied in the numerical examples. As the numerical results, the lowest three nondimensional frequency parameters are reported as functions of nondimensional system parameters; the load parameters, and the slenderness rations. And some typical mode shapes of free vibrations are also presented in figures.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.1015-1027
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• 2019

A class of systems of singularly perturbed convection diffusion type equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The suggested method is of almost first order convergence. An error estimate is derived in the discrete maximum norm. Numerical examples are presented to validate the theoretical estimates.