• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.177-196
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• 2022

The Elzaki Transform method is fuzzified to fuzzy Elzaki Transform by Rehab Ali Khudair. In this article, we propose a Double fuzzy Elzaki transform (DFET) method to solving fuzzy partial differential equations (FPDEs) and we prove some properties and theorems of DFET, fundamental results of DFET for fuzzy partial derivatives of the n^th order, construct the Procedure to find the solution of FPDEs by DFET, provide duality relation of Double Fuzzy Laplace Transform (DFLT) and Double Fuzzy Sumudu Transform(DFST) with proposed Transform. Also we solve the Fuzzy Poisson's equation and fuzzy Telegraph equation to show the DFET method is a powerful mathematical tool for solving FPDEs analytically.

• Kyungpook Mathematical Journal
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• v.21 no.1
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• pp.71-74
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• 1981

In this paper a general third order differential equation encountered in the flow of fluids in general and hopefully elsewhere. Sufficient conditions for existence & uniqueness of its solutions are given.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.623-631
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• 2005

The approximate controllability for the nonlinear control system with nonlinear monotone hemicontinuous and coercive operator is studied. The existence, uniqueness and a variation of solutions of the system are also given.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1163-1173
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• 2023

In this paper, we prove the Hyers-Ulam stability and Mittag-Leffler-Hyers-Ulam stability of a differential equation of Logistic growth in a population by applying Laplace transforms method.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.743-753
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• 2001

We provide local convergence results in affine form for inexact Newton-like as well as quasi-Newton iterative methods in a Banach space setting. We use hypotheses on the second or on the first and mth Frechet-derivative (m≥2 an integer) of the operator involved. Our results allow a wider choice of starting points since our radius of convergence can be larger than the corresponding one given in earlier results using hypotheses on the first-Frechet-derivative only. A numerical example is provided to illustrate this fact. Our results apply when the method is, for example, a difference Newton-like or update-Newton method. Furthermore, our results have direct applications to the solution of autonomous differential equations.

• Structural Engineering and Mechanics
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• v.41 no.2
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• pp.263-284
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• 2012

This paper aims to propose a computational technique for estimating the region of attraction (RoA) for autonomous nonlinear systems. To achieve this, the collocation method is applied to approximate the Lyapunov function by satisfying the modified Zubov's partial differential equation around asymptotically stable equilibrium points. This method is formulated for n-scalar differential equations with two classes of basis functions. In order to show the efficiency of the suggested approach, some numerical examples are solved. Moreover, the estimated regions of attraction are compared with two similar methods. In most cases, the proposed scheme can estimate the region of attraction more efficient than the other techniques.

• Journal of the Korean Society of Industry Convergence
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• v.3 no.1
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• pp.43-51
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• 2000

The response statistics of a hinged-clamped beam under broad-band random excitation is investigated. The random excitation is applied at the nodal point of the second mode. By using Galerkin's method the governing equation is reduced to a system of nonautonomous nonlinear ordinary differential equations. A method based upon the Markov vector approach is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The case of two mode interaction is considered in order to compare it with the case of three mode interaction. The analytical results for two and three mode interactions are also compared with results obtained by Monte Carlo simulation.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.261-280
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• 2005

We study the existence and nonexistence of positive periodic solutions of a non-autonomous functional differential equation with impulses. The equations we study may be of delay, advance or mixed type functional differential equations and the impulses may cause the existence of positive periodic solutions. The methods employed are fixed-point index theorem, Leray-Schauder degree, and upper and lower solutions. The results obtained are new, and some examples are given to illustrate our main results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.2
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• pp.337-345
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• 1997

An analysis is presented for the response of a beam constrained by a nonlinear spring to a harmonic excitation. The system is governed by a linear partial differential equation with a nonlinear boundary condition. The method of multiple scales is used to reduce the nonlinear boundary value problem to a system of autonomous ordinary differential equations of the amplitudes and phases. The case of the third-order subharmonic resonance is considered in this study. The autonomous system is used to determine the steady-state responses and their stability.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2023.05a
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• pp.252-253
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• 2023

Container terminal automation might offer many potential benefits, such as increased productivity, reduced cost, and improved safety. Autonomous trucks can lead to more efficient container transport. A robust lane detection method is proposed using score-based generative modeling through stochastic differential equations for image-to-image translation. Image processing techniques are combined with Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Genetic Algorithm (GA) to ensure lane positioning robustness. The proposed method is validated by a dataset collected from the port terminals under different environmental conditions and tested the robustness of the lane detection method with stochastic noise.