• 한국컴퓨터정보학회논문지
• /
• 제8권3호
• /
• pp.66-72
• /
• 2003

상미분 방정식은 물리학, 기계학, 전기학, 열역학 등에 많이 이용되는 방정식이나 수식이 복잡하고 처리 속도가 늦어서 실시간 처리에 어려움이 많다. 그래서 이 논문에서는 소프트웨어적인 방법으로는 많은 계산량으로 인하여 처리 속도가 떨어지므로 시스토릭어레이를 이용하여 Runge-Kutta 방법으로 상미분 값을 구하는 새로운 하드웨어를 제안하였다. 이 제안한 하드웨어는 처음 셀에서의 입력이 연속적으로 각 셀을 거치면서 처리되어 마지막셀에서는 상미분 값을 얻을 수 있다. 이렇게 처리함으로서 기존의 소프트웨어적인 방식에 비하여 수렴 속도도 빠르고 정확한 근사 값을 구할 수 있으므로 실시간 처리에 많이 이용될 수 있을 것이며, 기존의 다른 수치처리를 하는 하드웨어와 통합하여 사용될 수 있다. 이 논문에서는 제안한 하드웨어를 시뮬레이션하여 정확한 결과가 나오는 것을 확인하였다.

• Steel and Composite Structures
• /
• 제15권1호
• /
• pp.57-79
• /
• 2013

This paper studies the dynamic instability of laminated composite plates under thermal and arbitrary in-plane periodic loads using first-order shear deformation plate theory. The governing partial differential equations of motion are established by a perturbation technique. Then, the Galerkin method is applied to reduce the partial differential equations to ordinary differential equations. Based on Bolotin's method, the system equations of Mathieu-type are formulated and used to determine dynamic instability regions of laminated plates in the thermal environment. The effects of temperature, layer number, modulus ratio and load parameters on the dynamic instability of laminated plates are investigated. The results reveal that static and dynamic load, layer number, modulus ratio and uniform temperature rise have a significant influence on the thermal dynamic behavior of laminated plates.

• Journal of applied mathematics & informatics
• /
• 제41권2호
• /
• pp.401-411
• /
• 2023

The effects of longitudinal velocity dusty fluid flow in a weak magnetic field are investigated in this paper. An external uniform magnetic field parallel to the flow of dusty fluid influences the flow of dusty fluid. Besides that, the problem under investigation is completely defined in terms of identifying parameters such as longitudinal velocity (u), Hartmann number (M), dust particle interactions β, stock resistance γ, Reynolds number (Re) and magnetic Reynolds number (Rm). While using suitable transformations of resemblance, The governing partial differential equations are transformed into a system of ordinary differential equations. The Hankel Transformation is used to solve these equations numerically. The effects of representing parameters on the fluid phase and particle phase velocity flow are investigated in this analysis. The magnitude of the fluid particle is reduced significantly. The result indicates the magnitude of the particle reduced significantly. Although some of our numerical solutions agree with some of the available results in the literature review, other results differs because of the effect of the introduced magnetic field.

• Structural Engineering and Mechanics
• /
• 제57권2호
• /
• pp.327-355
• /
• 2016

A new analytical derivation of the elastodynamic point load solutions for an isotropic multi-layered half-space is presented by means of the precise integration method (PIM) and the approach of dual vector. The time-harmonic external load is prescribed either on the external boundary or in the interior of the solid medium. Starting with the axisymmetric governing motion equations in a cylindrical coordinate system, a second order ordinary differential matrix equation can be gained by making use of the Hankel integral transform. Employing the technique of dual vector, the second order ordinary differential matrix equation can be simplified into a first-order one. The approach of PIM is implemented to obtain the solutions of the ordinary differential matrix equation in the Hankel integral transform domain. The PIM is a highly accurate algorithm to solve sets of first-order ordinary differential equations and any desired accuracy of the dynamic point load solutions can be achieved. The numerical simulation is based on algebraic matrix operation. As a result, the computational effort is reduced to a great extent and the computation is unconditionally stable. Selected numerical trials are given to validate the accuracy and applicability of the proposed approach. More examples are discussed to portray the dependence of the load-displacement response on the isotropic parameters of the multi-layered media, the depth of external load and the frequency of excitation.

• 대한수학회논문집
• /
• 제36권3호
• /
• pp.549-555
• /
• 2021

We show the solvability of the ordinary differential equations describing curves on sphere or hyperbolic space. Making use of the geometric properties of the equations, we derive explicit solution formulae.

• Journal of applied mathematics & informatics
• /
• 제25권1_2호
• /
• pp.231-244
• /
• 2007

In this paper, we use measure theory for considering asymptotically stable of an autonomous system [1] of first order nonlinear ordinary differential equations(ODE's). First, we define a nonlinear infinite-horizon optimal control problem related to the ODE. Then, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then, the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measures. The optimal measure is approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this linear programming problem is used to find a piecewise-constant control, and by using the approximated control signals, we obtain the approximate trajectories and the error functional related to it. Finally the approximated trajectories and error functional is used to for considering asymptotically stable of the original problem.

• Journal of Information Processing Systems
• /
• 제14권2호
• /
• pp.455-468
• /
• 2018

The concepts of graph theory are applied to model and analyze dynamics of computer networks, biochemical networks and, semantics of social networks. The analysis of dynamics of complex networks is important in order to determine the stability and performance of networked systems. The analysis of non-stationary and nonlinear complex networks requires the applications of ordinary differential equations (ODE). However, the process of resolving input excitation to the dynamic non-stationary networks is difficult without involving external functions. This paper proposes an analytical formulation for generating solutions of nonlinear network ODE systems with functional decomposition. Furthermore, the input excitations are analytically resolved in linearized dynamic networks. The stability condition of dynamic networks is determined. The proposed analytical framework is generalized in nature and does not require any domain or range constraints.

• Journal of applied mathematics & informatics
• /
• 제28권3_4호
• /
• pp.845-862
• /
• 2010

In a recent paper, M.A. Noor et al. (Hindawi publishing corporation, Mathematical Problems in Engineering, Volume 2008, Article ID 696734, 11 pages, doi:10.1155/2008/696734) proposed the variational homotopy perturbation method (VHPM) for solving higher dimentional initial boundary value problems. In this paper, we consider the proposed method for analytic treatment of the linear and nonlinear ordinary differential equations, homogeneous or inhomogeneous. The results reveal that the proposed method is very effective and simple and can be applied for other linear and nonlinear problems in mathematical.

• Kyungpook Mathematical Journal
• /
• 제32권3_spc호
• /
• pp.311-320
• /
• 1992

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