• 호남수학학술지
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• 제35권4호
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• pp.683-699
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• 2013

In this paper, an improved ($\frac{G^{\prime}}{G}$)-expansion method is proposed for obtaining travelling wave solutions of nonlinear evolution equations. The proposed technique called ($\frac{F}{G}$)-expansion method is more powerful than the method ($\frac{G^{\prime}}{G}$)-expansion method. The efficiency of the method is demonstrated on a variety of nonlinear partial differential equations such as KdV equation, mKd equation and Boussinesq equations. As a result, more travelling wave solutions are obtained including not only all the known solutions but also the computation burden is greatly decreased compared with the existing method. The travelling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. The result reveals that the proposed method is simple and effective, and can be used for many other nonlinear evolutions equations arising in mathematical physics.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.65-77
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• 2013

In this paper, we develop the operational Tau method for solving nonlinear Volterra integro-differential equations of the second kind. The existence and uniqueness of the problem is provided. Here, we show that the nonlinear system resulted from the operational Tau method has a semi triangular form, so it can be solved easily by the forward substitution method. Finally, the accuracy of the method is verified by presenting some numerical computations.

• Korean Journal of Mathematics
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• 제25권3호
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• pp.323-334
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• 2017

In this paper, we propose a combined form for solving nonlinear interval Volterra-Fredholm integral equations of the second kind based on the modifying Laplace Adomian decomposition method. We find the exact solutions of nonlinear interval Volterra-Fredholm integral equations with less computation as compared with standard decomposition method. Finally, an illustrative example has been solved to show the efficiency of the proposed method.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 ITC-CSCC -2
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• pp.898-901
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• 2000

A new 2-D block Kalman filtering method which uses a nonlinear function is presented to generate a more accurate filtered estimate of a range image that has been corrupted by additive noise. Novel 2-D block Kalman filtering method is constructed of the conventional method and nonlinear function which utilizes to control estimation error. We show that novel 2-D Kalman filtering method using a nonlinear function is effective at reducing the additive noise, not distorting shape edges.

• 한국지진공학회논문집
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• 제10권4호
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• pp.55-66
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• 2006

본 연구에서는 강성골격곡선으로부터 산정한 구조물의 초기 탄성진동주기 $T_1$와 응답스트럼으로부터 산정한 비선형 유사가속도 $A_{1y}/g$ 및 연성비 ${\mu}$를 사용하여, 반복적인 계산과정 없이 복합구조물의 내진성능을 평가하는 비선형직접스펙트럼법(NDSM)을 고려한다. 다양한 지진과 복합구조물에 대한 NDSM의 신뢰성과 실용성을 비선형시각이력해석(NRHA) 결과와 비교 검토하였다. 본 연구의 결론은 다음과 같다. (1) NDSM은 강성골격곡선으로부터 기본진동주기와 비선형 항복강도를 구하면, 비선형 응답스펙트럼으로부터 직접적으로 구조물의 비선형 최대응답을 산정할 수 있는 실용적인 방법으로 사료된다. (2) NDSM의 응답을 정산해와 비교한 결과, 대부분의 모델이 단순평균의 관점에서 전체 해석모델 중 3/4이 약 20% 이하의 오차를 나타내었고, 일반적으로 비선형시각이력해석의 응답보다 크게 산정되는 것으로 나타났다.

• 한국소음진동공학회논문집
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• 제16권8호
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• pp.814-821
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• 2006

A structural coupling method is developed for the dynamic analysis of a nonlinear structure with concentrated nonlinear hinge joints or sliding lines. The component mode synthesis method is extended to couple substructures and the nonlinear models. In order to verify the improved coupling method, a numerical plate model consisting of two substructures and torsional springs, is synthesized by using the proposed method and its modal parameters are compare with analysis data. Then the coupling method is applied to a three-substructure-model with the nonlinearity of sliding lines between the substructures. The coupled structural model is verified from its dynamic analysis. The analysis results show that the improved coupling method is adequate for the structural nonlinear analyses with the nonlinear hinge and sliding mode condition.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2001년도 하계종합학술대회 논문집(3)
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• pp.17-20
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• 2001

In this paper, we design a nonlinear adaptive controller using wavelet neural network. The method proposed in this paper performs for a nonlinear system with unknown parameters, identification with using a wavelet neural network, and then a nonlinear adaptive controller is designed with those identified informations. The advantage of the proposed control method is simple to design a controller for unknown nonlinear systems, because we use the identified informations and design parameters are positioned within a negative real part of s-plane. The simulation results showed the effectiveness of proposed controller design method.

• 전기의세계
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• 제22권2호
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• pp.40-44
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• 1973

A method for obtaining state equation for nonlinear time-varying RLC networks is presented. The nonlinear time-varying RLC elements are decomposed by using Murata method to formulate nonlinear state equation. A nonlinear time-varying RLC network containing twin tunnel diode is solved as an example. In consequence of solving the examjple, simple methods are presented for revising the original network model so that the formulation of state equation is simplified.

• 충청수학회지
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• 제7권1호
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• pp.141-152
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• 1994

We consider a numerical scheme for solving a nonlinear boundary integral equation (BIE) obtained by reformulation the nonlinear boundary value problem (BVP). We give a simple alternative to the standard collocation method for the nonlinear BIE. This method consists of one conventional linear system and another coupled linear system resulting from an auxiliary BIE which is obtained by differentiating both side of the nonlinear interior integral equations. We obtain an analogue BIE through the perturbation of the fundamental solution of Laplace's equation. We procure the super-convergence of approximate solutions.

• Journal of Mechanical Science and Technology
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• 제16권6호
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• pp.819-828
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• 2002

An analytical method is presented for evaluation of the steady state periodic behavior of nonlinear systems. This method is based on the substructure synthesis formulation and a MS (multiple scales) procedure, which is applied to the analysis of nonlinear responses. The proposed procedure reduces the size of large degrees-of-freedom problem in solving nonlinear equations. Feasibility and advantages of the proposed method are illustrated with the nonlinear rotating machine system as an example of large mechanical structure systems. In addition, its efficiency for nonlinear response prediction will be shown by comparison of other conventional methods.