• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.435-459
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• 2004

Identification problems for the system governed by abstract nonlinear damped second order evolution equations are studied. Since unknown parameters are included in the diffusion operator, we can not simply identify them by using the usual optimal control theories. In this paper we present how to solve our identification problems via the method of transposition.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.223-235
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• 2006

By applying the Landau-type transformation, we transform a Stefan problem with nonlinear free boundary condition into a system consisting of a parabolic equation and the ordinary differential equations. Fully discrete finite element method is developed to approximate the solution of a system of a parabolic equation and the ordinary differential equations. We derive optimal orders of convergence of fully discrete approximations in $L_2,\;H^1$ and $H^2$ normed spaces.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.167-183
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• 2002

A modified discretization ABS algorithm for solving a class of singular nonlinear systems, F($\chi$)=0, where $\chi$, F $\in$ $R^n$, is presented, constructed by combining a discretization ABS algorithm arid a method of Hoy and Schwetlick (1990). The second order differential operation of F at a point is not required to be calculated directly in this algorithm. Q-quadratic convergence of this algorithm is given.

• Honam Mathematical Journal
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• v.31 no.1
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• pp.75-85
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• 2009

We show the existence of the nontrivial periodic solution for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition by critical point theory and linking arguments. We investigate the geometry of the sublevel sets of the corresponding functional of the system, the topology of the sublevel sets and linking construction between two sublevel sets. Since the functional is strongly indefinite, we use the linking theorem for the strongly indefinite functional and the notion of the suitable version of the Palais-Smale condition.

• East Asian mathematical journal
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• v.35 no.3
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• pp.341-349
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• 2019

In this paper, we are concerned with the minimal positive solution to system of the nonlinear matrix equations $A_1X^2+B_1Y +C_1=0$ and $A_2Y^2+B_2X+C_2=0$, where $A_i$ is a positive matrix or a nonnegative irreducible matrix, $C_i$ is a nonnegative matrix and $-B_i$ is a nonsingular M-matrix for i = 1, 2. We apply Newton's method to system and present a modified Newton's iteration which is validated to be efficient in the numerical experiments. We prove that the sequences generated by the modified Newton's iteration converge to the minimal positive solution to system of nonlinear matrix equations.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.449-471
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• 2023

In this paper, we study a linear system of homogeneous commensurate /incommensurate fractional-order differential equations by developing a new semi-analytical scheme. In particular, by decoupling the system into two fractional-order differential equations, so that the first equation of order (δ + γ), while the second equation depends on the solution for the first equation, we have solved the under consideration system, where 0 < δ, γ ≤ 1. With the help of using the Adomian decomposition method (ADM), we obtain the general solution. The efficiency of this method is verified by solving several numerical examples.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.39 no.9
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• pp.805-815
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• 2011

Nonlinear Parabolized Stability Equations(NSPE) can be effectively used to study more throughly the transition process. NPSE can efficiently analyze the stability of a nonlinear region in transition process with low computational cost compared to Direct Numerical Simulation(DNS). In this study, NPSE in general coordinate system is formulated and a computer code to solve numerically the equations is developed. Benchmark problems for incompressible and compressible boundary layers over a flat plate are analyzed to validate the present code. It is confirmed that the NPSE methodology constructed in this study is an efficient and effective tool for nonlinear stability analysis.

• Coupled systems mechanics
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• v.7 no.6
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• pp.707-729
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• 2018

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.489-496
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• 2004

We study the h- stability of nonlinear difference system x(n+1) =f(n, x(n)) and its perturbed system y(n+l) =f(n, y(n))+g(n, y(n), Sy(n)).

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2001.09a
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• pp.243-250
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• 2001

Industrial machines are sometimes exposed to the danger of earthquake. In the design of a mechanical system, this factor should be accounted for from the viewpoint of reliability. A method to analyze a complex nonlinear structure system under random excitation is proposed. First, the actual random excitation, such as earthquake, is approximated to the corresponding Gaussian process far the statistical analysis. The modal equations of overall system are expanded sequentially. Then, the perturbed equations are synthesized into the overall system and solved in probabilistic way. Several statistical properties of a random process that are of interest in random vibration applications are reviewed in accordance with nonlinear stochastic problem. The obtained statistical properties of the nonlinear random vibration are evaluated in each substructure. Comparing with the results of the numerical simulation proved the efficiency of the proposed method.