• Journal of Korea Water Resources Association
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• v.33 no.S1
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• pp.101-110
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• 2000

This paper introduces the equivalent frequency response method(EFRM) into runoff analysis. This EFRM originally had been developed to analyze dynamic behavior of nonlinear elements such as threshold and saturation in control engineering. Many runoff models are described by nonlinear ordinary of partial differential equations This paper presents that these nonlinear differential equations can be converted into semi-linear ones based on EFRM. The word of "a semi-linear equation" means that the coefficients of derived equations depend on average rainfall.

• Proceedings of the Korea Water Resources Association Conference
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• 2000.05a
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• pp.1-2
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• 2000

This paper introduces the equivalent frequency response method (EFRM) into runoff analysis. This EFRM originally had been developed to analyze dynamic behavior of nonlinear elements such as threshold and saturation in control engineering. Many runoff models are described by nonlinear ordinary or partial differential equations. This paper presents that these nonlinear differential equations can be converted into semi-linear ones based on EFRM. The word of “a semi-linear equation” means that the coefficients of derived equations depend on average rainfall

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.224-261
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• 2021

The interest in implicit-explicit (IMEX) integration methods has emerged as an alternative for dealing in a computationally cost-effective way with stiff ordinary differential equations arising from practical modeling problems. In this paper, we introduce implicit-explicit second derivative linear multi-step methods (IMEX SDLMM) with error control. The proposed IMEX SDLMM is based on second derivative backward differentiation formulas (SDBDF) and recursive SDBDF. The IMEX second derivative schemes are constructed with order p ranging from p = 1 to 8. The methods are numerically validated on well-known stiff equations.

• Steel and Composite Structures
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• v.31 no.2
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• pp.187-199
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• 2019

This paper presents the semi-analytical development of the dynamic instability behavior and the dynamic response of functionally graded (FG) cylindrical shallow shell panel subjected to different type of periodic axial compression. First, in prebuckling analysis, the stresses distribution within the panels are determined for respective loading type and these stresses are used to study the dynamic instability behavior and the dynamic response. The prebuckling stresses within the shell panel are the same as applied in-plane edge loading for the case of uniform and linearly varying loadings. However, this is not true for the case of parabolic loadings. The parabolic edge loading produces all the stresses (${\sigma}_{xx}$, ${\sigma}_{yy}$ and ${\tau}_{xy}$) within the FG cylindrical panel. These stresses are evaluated by minimizing the membrane energy via Ritz method. Using these stresses the partial differential equations of FG cylindrical panel are formulated by applying Hamilton's principal assuming higher order shear deformation theory (HSDT) and von-$K{\acute{a}}rm{\acute{a}}n$ non-linearity. The non-linear governing partial differential equations are converted into a set of Mathieu-Hill equations via Galerkin's method. Bolotin method is adopted to trace the boundaries of instability regions. The linear and non-linear dynamic responses in stable and unstable region are plotted to know the characteristics of instability regions of FG cylindrical panel. Moreover, the non-linear frequency-amplitude responses are obtained using Incremental Harmonic Balance (IHB) method.

• Journal of Advanced Marine Engineering and Technology
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• v.15 no.4
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• pp.46-53
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• 1991

In the present study, Navier-Stokes equation is numerically solved by use of a Finite analytic method to obtain the 2-dimensional flow field in the square cavity. The basic idea of F.A.M. is the incorporation of local analytic solutions in the numerical solution of linear or non-linear partial differential equations. In the F.A.M., the total problem is subdivided into a number of all elements. The local analytic solution is obtained for the small element in which the governing equation, if non-linear, to be linearized. The local analytic solutions are then expressed in algebraic form and are overlapped to cover the entire region of the problem. The assembly of these local analytic solutions, which still preserve the overall nonlinearity of the governing equations, results in a system of linear algebraic equations. The system of algebraic equations is then solved to provide the numerical solutions of the total problem. The computed flow field shows the same characteristics to physical concept of flow phenomena.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.689-696
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• 2006

This paper deals with the geometrical non-linear analyses of the buckled columns. Differential equations governing elasticas of the buckled columns are derived, in which both effects of taper type and shear deformation are included. Three kinds of taper types such as breadth, depth and square tapers are considered. Differential equations are solved numerically to obtain the elasticas and buckling loads of such columns. End constraint of both clamped ends and both hinged ends are considered. The effects of shear deformation on the elastica of the buckled column and buckling load of column are investigated extensively. Experimental studies are presented that complement theoretical results of non-linear responses of the elasticas.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.845-862
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• 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.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.45 no.3
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• pp.399-406
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• 1996

This paper presents a method of hierarchical state estimation of the time-varying linear systems via Block-pulse function(BPF). When we estimate the state of the systems where noise is considered, it is very difficult to obtain the solutions because minimum error variance matrix having a form of matrix nonlinear differential equations is included in the filter gain calculation. Therefore, hierarchical approach is adapted to transpose matrix nonlinear differential equations to a sum of low order state space equation from and Block-pulse functions are used for solving each low order state space equation in the form of simple and recursive algebraic equation. We believe that presented methods are very attractive nd proper for state estimation of time-varying linear systems on account of its simplicity and computational convenience. (author). 13 refs., 10 figs.

• Journal of the Korean Mathematical Society
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• v.26 no.2
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• pp.167-173
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• 1989

• Bulletin of the Korean Mathematical Society
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• v.17 no.1
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• pp.1-7
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• 1980