• Journal of Mechanical Science and Technology
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• 제14권2호
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• pp.168-176
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• 2000

Related to the error dynamics of an adaptive system, averaging theorems are developed for coupled differential equations which consist of ordinary differential equations and a parabolic partial differential equation. The results are then applied to the convergence analysis of the parameter estimate errors in the model reference adaptive control of a nonautonomous parabolic partial differential equation with lowly time-varying parameters.

• 제어로봇시스템학회논문지
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• 제9권7호
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• pp.556-562
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• 2003

This paper presents new attitude error differential equations to define attitude errors as the rotation vector for inertial navigation systems. Attitude errors are defined with the rotation vector between the reference coordinate frame and the platform coordinate frame, and Platform dynamics to the reference coordinate frame due to platform torque command errors are defined. Using these concepts for attitude error definition and platform dynamics, we have derived attitude error differential equations expressed in original nonlinear form for GINS and SDINS and showed that these are equivalent to attitude error differential equations expressed in known linear form. The relation between attitude errors defined by the rotation vector and attitude errors defined by quaternion is clearly presented as well.

• Nuclear Engineering and Technology
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• 제55권3호
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• pp.861-869
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• 2023

This article proposes a novel approach to measure the performance of Safety-Critical Systems (SCS). Such systems contain multiple processing nodes that communicate with each other is modeled by a Petri nets (PN). The paper uses the PN for the performance evaluation of SCS. A set of ordinary differential equations (ODEs) is derived from the Petri net model that represent the state of the system, and the solutions can be used to measure the system's performance. The proposed method can avoid the state space explosion problem and also introduces new metrics of performance, along with their measurement: deadlock, liveness, stability, boundedness, and steady state. The proposed technique is applied to Shutdown System (SDS) of Nuclear Power Plant (NPP). We obtained 99.887% accuracy of performance measurement, which proves the effectiveness of our approach.

• Journal of applied mathematics & informatics
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• 제37권5_6호
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• pp.329-339
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• 2019

The Banach spaces $m^p(\phi)$ and $n^p(\phi)$ are very important sequence spaces related to $l_p$, which were defined to fill the gaps between $l_p(1{\leq}p{\leq}{\infty})$. In this paper, we investigated the solubility of the infinite system of differential equations in $m^p(\phi)$ and $n^p(\phi)$ by proving related theorems. Moreover, one example has been included for the justification of the claim of this paper.

• 한국산업융합학회 논문집
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• 제3권1호
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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.

• 호남수학학술지
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• 제37권3호
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• pp.299-315
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• 2015

In this paper, we study the first-order system least-squares (FOSLS) spectral method for parabolic partial differential equations. There were lots of least-squares approaches to solve elliptic partial differential equations using finite element approximation. Also, some approaches using spectral methods have been studied in recent. In order to solve the parabolic partial differential equations in parallel, we consider a parallel numerical method based on a hybrid method of the frequency-domain method and first-order system least-squares method. First, we transform the parabolic problem in the space-time domain to the elliptic problems in the space-frequency domain. Second, we solve each elliptic problem in parallel for some frequencies using the first-order system least-squares method. And then we take the discrete inverse Fourier transforms in order to obtain the approximate solution in the space-time domain. We will introduce such a hybrid method and then present a numerical experiment.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권2호
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• pp.109-121
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• 2009

In this paper, we use He's polynomials for solving higher order integro differential equations (IDES) by converting them to an equivalent system of integral equations. The He's polynomials which are easier to calculate and are compatible to Adomian's polynomials are found by using homotopy perturbation method. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Several examples are given to verify the reliability and efficiency of the proposed method.

• 대한전자공학회논문지
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• 제16권5호
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• pp.18-26
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• 1979

본 논문에서는 algebraic matrix Lyapunov equations과 a1gebraic matrix Riccati equations에 관하여 잘 알려져 있는 중요한 결과를 확장한다. 본 연구는 Matrix 미분 방정식에서 양단 경계조건이 존재하는 문제를 다루며 여기에서 얻어지는 결과는 기존하고 있는 결과를 포함하게 된다. 특히 선형 시스템이 periodic feedback gain control로 안정화되는 필요충분조건을 구하며, two-point boundary Riccati equations의 해를 쉽게 구하는 반복 계산방법을 제시한다. 또한 interalwise reeceding horizon을 이용한 새로운 periodic feedback gain control이 시스템을 안전화시켜줌을 보여준다.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1279-1292
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• 2009

In this paper, a numerical method that uses standard finite difference scheme defined on Shishkin mesh for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a discontinuous source term is presented. An error estimate is derived to show that the method is uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented to illustrate the theoretical results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제3권1호
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• pp.83-94
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• 1996

Classical mechanics begins with some variants of Newton's laws. Lagrangian mechanics describes motion of a mechanical system in the configuration space which is a differential manifold defined by holonomic constraints. For a conservative system, the equations of motion are derived from the Lagrangian function on Hamilton's variational principle as a system of the second order differential equations. Thus, for conservative systems, Newtonian mechanics is a particular case of Lagrangian mechanics.(omitted)