• Earthquakes and Structures
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• v.13 no.2
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• pp.131-136
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• 2017

This paper concerns two new analytical approaches for solving high nonlinear vibration equations. Energy Balance method and Hamiltonian Approach are presented and successfully applied for nonlinear vibration equations. In these approaches, there is no need to use small parameters to solve and only with one iteration, high accurate results are reached. Numerical procedures are also presented to compare the results of analytical and numerical ones. It has been established that, the proposed approaches are in good agreement with numerical solutions.

• Steel and Composite Structures
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• v.25 no.4
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• pp.497-503
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• 2017

In this paper, nonlinear vibration of multi-degree of freedom systems are studied. It has been tried to develop the mathematical model of systems by second-order nonlinear partial differential equations. The masses are connected with linear and nonlinear springs in series. A great effort has been done to solve the nonlinear governing equations analytically. A new analytical method called Variational Iteration Method (VIM) is proposed and successfully applied to the problem. The linear and nonlinear frequencies are obtained and the results are compared with numerical solutions. The first order of Variational Iteration Method (VIM) leads us to high accurate solution.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.883-893
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• 2011

In this paper we study h-stability of the solutions of nonlinear difference system via the notion of $n_{\infty}$-summable similarity between its variational systems. Also, we show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent. Furthermore, we characterize h-stability for nonlinear difference systems by using Lyapunov functions.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.1-4
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• 2003

This paper we study the existence of a global solution for the nonlinear fuzzy differential equations in E$_{N}$$^{n}$ by using the concept of fuzzy number of dimension n whose values are normal, convex, upper semicontinuous and compactly supported surface in R$^{n}$ . .

• 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.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.773-785
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• 2012

In this paper, we establish sufficient conditions for the existence and uniqueness of solutions to a general class of three-point boundary value problems for a coupled system of nonlinear fractional differential equations. The differential operator is taken in the Caputo fractional derivatives. By using Green's function, we transform the derivative systems into equivalent integral systems. The existence is based on Schauder fixed point theorem and contraction mapping principle. Finally, some examples are given to show the applicability of our results.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.8
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• pp.715-719
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• 2001

In this paper, we study the existence and uniqueness of fuzzy solution for the nonlinear fuzzy differential equations with nonlocal initial condition in E$^{2}$$_{N}$

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.8
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• pp.726-730
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• 2001

In this paper, we consider the observability conditions for the following nonlinear fuzzy neutral functional differential equations in E$^{2}$$_{N}$.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.179-193
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• 2005

We present results of fully nonlinear time-dependent simulations of a thin liquid film flowing up an inclined plane. Equations of the type $h_t+f_y(h) = -{\in}^3{\nabla}{\cdot}(M(h){\nabla}{\triangle}h)$ arise in the context of thin liquid films driven by a thermal gradient with a counteracting gravitational force, where h = h(x, t) is the fluid film height. A hybrid scheme is constructed for the solution of two-dimensional higher-order nonlinear diffusion equations. Problems in the fluid dynamics of thin films are solved to demonstrate the accuracy and effectiveness of the hybrid scheme.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1697-1710
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• 2014

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Meanwhile, under the condition of the positive initial energy, it is showed that the solutions blow up in the finite time and the lifespan estimate of solutions is also given.