• Journal of the Korea Society of Computer and Information
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• v.26 no.1
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• pp.69-76
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• 2021

Recentlly neural network approach for solving a singular perturbed integro-differential boundary value problem have been researched. Especially the model of the feed-forward neural network to be trained by the back propagation algorithm with various learning algorithms were theoretically substantiated, and neural network models such as deep learning, transfer learning, federated learning are very rapidly evolving. The purpose of this paper is to study the approaching method for developing a neural network model with high accuracy and speed for solving singular perturbed problem along with asymptotic methods. In this paper, we propose a method that the simulation for the difference between result value of singular perturbed problem and unperturbed problem by using neural network approach equation. Also, we showed the efficiency of the neural network approach. As a result, the contribution of this paper is to show the possibility of simple neural network approach for singular perturbed problem solution efficiently.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.3
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• pp.39-49
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• 2003

The delta operator approach and the singular perturbation technique are introduced. The former reduces the round-off error in the numerical computation. The latter reduces computing time by decoupling the original system into the fast and slow sub-systems. The aircraft dynamics consists of the Phugoid and short-period motions whether its model is longitudinal or lateral. In this paper, an approximated solutions of lateral dynamic model of Beaver obtained by using those two methods in compared with the exact solution. For open-loop system and closed-loop system, and approximated solution gets identical to the exact solution with only one iteration and without iteration, respectively. Therefore, it is shown that implementing those approaches is very effective in the flight dynamic and control.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.458-463
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• 2000

The mechanical structures generally have discontinuous parts such as the cracks, notches and holes owing to various reasons. In this paper, in order to analyze effectively these singularity problems using the finite element method, a mixed analysis method which an analytical solution and finite element solutions are simultaneously used is newly proposed. As the analytical solution is used in the singularity region and the finite element solutions are used in the remaining regions except this singular zone, this analysis method reasonably provides for the numerical solution of a singularity problem. Through various numerical examples, it is shown that the proposed analysis method is very convenient and gives comparatively accurate solution.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1273-1287
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• 2008

In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1297-1301
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• 1997

Generally, singularity analysis of 6-DOF parallerl manipulators is very difficult and, as result, velocity relation has many uncertainties. In this paper, an alternative method using the local structurizatioin method(LSM) for the analysis of singular configuraions is presented. With LSM, the velocity relation can be represented in a simple form, and the result is totally equivalent to the conventional velocity relation. The velocity relation suggested in this paper gives a closed-form solution of singularities.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.441-452
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• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.5
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• pp.883-890
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• 1992

Analysis of dynamic or impact problems is very important in engineering fields such as airplanes and automobiles. In the present study, two-dimensional elastodynamic BEM program with Laplace transformation is developed to analyze dynamic or impact problems. Accuracy and efficiency of the BEM program are tested by making the comparision of impact analysis of some models with other's published results. The BEM developed is applied to the impact crack problem and the dynamic stress intensity factors of some impact cracks is obtained by the displacement extrapolation method. It is confirmed to be possible to analyze impact problems accurately with only a little elements in simple models. And also it is found to be careful to use the singular element usually using in static crack problems because that the elastodynamic fundamental solution usually using in static crack problems because that the elastodynamic fundamental solution has more sensitive singularity than the static fundamental solution and to determine the boundary conditions in dynamic problems.

• Structural Engineering and Mechanics
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• v.76 no.4
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• pp.505-512
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• 2020

This paper presents an error estimation technique for 2-D crack analysis by an enriched natural element (more exactly, enriched Petrov-Galerkin NEM). A bare solution was approximated by PG-NEM using Laplace interpolation functions. Meanwhile, an accurate quasi-exact solution was obtained by a combined use of enriched PG-NEM and the global patch recovery. The Laplace interpolation functions are enriched with the near-tip singular fields, and the approximate solution obtained by enriched PG-NEM was enhanced by the global patch recovery. The quantitative error amount is measured in terms of the energy norm, and the accuracy (i.e., the effective index) of the proposed method was evaluated using the errors which obtained by FEM using a very fine mesh. The error distribution was investigated by calculating the local element-wise errors, from which it has been found that the relative high errors occurs in the vicinity of crack tip. The differences between the enriched and non-enriched PG-NEMs have been investigated from the effective index, the error distribution, and the convergence rate. From the comparison, it has been justified that the enriched PG-NEM provides much more accurate error information than the non-enriched PG-NEM.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.591-612
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• 2021

In this paper, a uniformly convergent numerical scheme is designed for solving singularly perturbed reaction-diffusion problems. The problem is converted to an equivalent weak form and then a Galerkin finite element method is used on a piecewise uniform Shishkin mesh with linear basis functions. The convergence of the developed scheme is proved and it is shown to be almost fourth order uniformly convergent in the maximum norm. To exhibit the applicability of the scheme, model examples are considered and solved for different values of a singular perturbation parameter ε and mesh elements. The proposed scheme approximates the exact solution very well.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.6
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• pp.820-832
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• 1986

In contrast to conventional liquid phase epitaxy of GaAs, surface kinetics limited growth is predominant in selective liquid phase epitaxy. For the stripe openings in the high-index crystal-lographic directions, the well-known facet formations and the decompositions into the low index planes or smooth circular surfaces are observed depending on the growth kinetics. For the low index direction stripe, surface kinetics limited growth is evident. By a numerical calcualtion we show that these phenomena are due to the enhanced masstransport by two dimensional diffusion and growth rate anisotropy which is found to be very stdrong with cusped minima for some singular planes in the solution growth as well as in vapor phase epitaxy. Morphological stability is briefly treated in terms of diffusion and its implications on device application are stated. Tese phenomena may be common to III-V compound semiconductors as well as GaAs.