• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.165-180
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• 2001

This paper presents a new difference scheme for numerical solution of stiff system of ODE’s. The present study is mainly motivated to develop an absolutely stable numerical method with a high order of approximation. In this work a double implicit A-stable difference scheme with the sixth order of approximation is suggested. Another purpose of this study is to introduce automatic choice of the integration step size of the difference scheme which is derived from the proposed scheme and the one step scheme of the fourth order of approximation. The algorithm was tested by means of solving the Kreiss problem and a chemical kinetics problem. The behavior of the gas explosive mixture (H₂+ O₂) in a closed space with a mobile piston is considered in test problem 2. It is our conclusion that a hydrogen-operated engine will permit to decrease the emitted levels of hazardous atmospheric pollutants.

• Nuclear Engineering and Technology
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• v.31 no.1
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• pp.80-87
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• 1999

An analytic axial xenon oscillation model was developed for pressurized water reactor analysis. The model employs an equation system for axial difference parameters that was derived from the two-group one-dimensional diffusion equation with control rod modeling and coupled with xenon and iodine balance equations. The spatial distributions of nu, xenon, and iodine were expanded by the Fourier sine series, resulting in cancellation of the flux-xenon coupled non-linearity. An inhomogeneous differential equation system for the axial difference parameters, which gives the relationship between power, iodine and xenon axial differences in the case of control rod movement, was derived and solved analytically. The analytic solution of the axial difference parameters can directly provide with the variation of axial power difference during xenon oscillation. The accuracy of the model is verified by benchmark calculations with one-dimensional reference core calculations.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1067-1082
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• 2013

In this paper, we will find some recurrence relations of classical multiple OPS between the same family with different parameters using the generating functions, which are useful to find structure relations and their connection coefficients. In particular, the differential-difference equations of Jacobi-Pineiro polynomials and multiple Bessel polynomials are given.

• ETRI Journal
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• v.23 no.2
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• pp.71-76
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• 2001

In this paper, the electromagnetic characteristics of a grounded slab and a parallel-plate structure are analyzed by the Spline-type Divided-Difference Interpolation (SDDI) technique. The technique efficiently evaluates the MoM impedance matrix elements of the multifold spectral or spatial domain integrals or summation in integro differential equations. The numerical results of the proposed method agree well with those of the corresponding literatures.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.449-465
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• 1994

The two common numerical methods to approximate the solution of partial differential equations are the finite element method and the finite difference method. They both lead to solving large sparse linear systems. For many applications, it is not unusal that the order of matrix is greater than 10, 000. For this kind of problem, a direct method such as Gaussian elimination can not be used because of the prohibitive cost. To this end, many iterative methods with modest cost have been studied and proposed by numerical analysts.(omitted)

• Proceedings of the KIPE Conference
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• 1998.10a
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• pp.34-39
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• 1998

This paper describes the simulation approaches employed for a vector control system of induction motor drive using SIMNON for windows program. SIMNON program tool can solve differential and difference equations for nonlinear dynamical control system. One powerful feature is its ability of allowing integration of individual program modules after each individual module is programed and tested independently. This particular feature is exploited here for an SVPWM inverter drive by real-time modeling and simulation. The suggested programs are provided a simple and complete simulation for induction motor vector drive system.

• Computers and Concrete
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• v.25 no.6
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• pp.537-549
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• 2020

Geometrically nonlinear axisymmetric bending analysis of shear deformable circular plates on a nonlinear three-parameter elastic foundation was made. Plates ranging from "thin" to "moderately thick" were investigated for three types of material: isotropic, transversely isotropic, and orthotropic. The differential equations were discretized by means of the finite difference method (FDM) and the differential quadrature method (DQM). The Newton-Raphson method was applied to find the solution. A parametric investigation using seven unknowns per node was presented. The novelty of the paper is that detailed numerical simulations were made to highlight the combined effects of the material properties and the boundary conditions on (i) the deflection, (ii) the stress resultants, and (iii) the external load. The formulation was verified through comparison studies. It was observed that the results are highly influenced from the boundary conditions, and from the material properties.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.3
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• pp.189-200
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• 2010

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.4
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• pp.8-15
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• 2011

In this paper, the influence of a crack on the natural frequency of cracked cantilever L-shaped beam with coupled bending and torsional vibrations by analytically and experimentally is analyzed. The L-shaped beam with a crack is modeled by Hamilton's principle with consideration of bending and torsional energy. The two coupled governing differential equations are reduced to one sixth-order ordinary differential equation in terms of the flexural displacement. The crack is assumed to be in the first, second and third mode of fracture and to be always opened during the vibrations. The theoretical results are validated by a comparison with experimental measurements. The maximal difference between the theoretical results and experimental measurements of the natural frequency is less than 7.5% in the second vibration mode.

• Interaction and multiscale mechanics
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• v.5 no.4
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• pp.369-383
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• 2012

In this paper, soil-structure interaction analysis has been presented for beams resting on multilayered geosynthetic-reinforced granular fill-soft soil system. The soft soil and geosynthetic reinforcements are idealized as nonlinear springs and elastic membranes, respectively. The governing differential equations are solved by finite difference technique and the results are presented in non-dimensional form. It is observed from the study that use of geosynthetic reinforcement is not very effective for maximum settlement reduction in case of very rigid beam. Similarly the reinforcements are not effective for shear force reduction if the granular fill has very high shear modulus value. However, multilayered reinforced system is very effective for bending moment and differential settlement reduction.