• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.22 no.4
• /
• pp.289-294
• /
• 2018

In this work, a recently developed semi-analytic technique, so called the residual power series method, is generalized to process higher-dimensional linear and nonlinear partial differential equations. The solutions obtained takes a form of an infinite power series which can, in turn, be expressed in a closed exact form. The results reveal that the proposed generalization is very effective, convenient and simple. This is achieved by handling the (m+1)-dimensional Burgers equation.

• Journal of applied mathematics & informatics
• /
• v.37 no.5_6
• /
• pp.429-442
• /
• 2019

This article addresses the influence of partial slip condition in the hydromagnetic flow of Burgers fluid in a rotating frame of reference.The flows are induced by oscillation of a boundary. Two problems for oscillatory flows are considered. Exact solutions to the resulting boundary value problems are constructed. Analysis has been carried out in the presence of magnetic field. Physical interpretation is made through the plots for various embedded parameters.

• Proceedings of the KSR Conference
• /
• 2004.06a
• /
• pp.1308-1312
• /
• 2004

Transmission line impedance calculation has been tried for obtaining exact value. The method proposed by Carson contains indefinite complex integral. Although the Carson solution is proposed with power series, the solution is limited and valid at special range of frequency. In this paper, we proposed a simplified Carson solution by analytical method using ground transmission line return current. This method calculate the transmission line impedance easily.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.6 no.2
• /
• pp.85-97
• /
• 2002

In this paper, finite volume element methods for nonlinear parabolic problems are proposed and analyzed. Optimal order error estimates in $W^{1,p}$ and $L_p$ are derived for $2{\leq}p{\leq}{\infty}$. In addition, superconvergence for the error between the approximation solution and the generalized elliptic projection of the exact solution (or and the finite element solution) is also obtained.

• Water for future
• /
• v.16 no.2
• /
• pp.123-129
• /
• 1983

One of the techniques to determine flood stages in natural channel is to find the solution of unsteady flow equations such as continuity and momentum equations. Since the exact analytic solution of these equations are not Known, the implicit numerical scheme is widely accepted tool for the approximate solution of equations. This technique is applied to the downstream of Daechung Dam in Geum River for the determination of flood stage for given frequency. However the flood stages are greatly affected by the method of reservoir Operation Method and Technical Operation Reservoir Method. Obviously, the Tech. ROM is found to be superior to Auto ROM.

• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.217-229
• /
• 2007

In this paper, Genetic Algorithm (GA) is used to find the Maximum Weight Independent Set (MWIS) of a graph. First, MWIS problem is formulated as a 0-1 integer programming optimization problem with linear objective function and a single quadratic constraint. Then GA is implemented with the help of this formulation. Since GA is a heuristic search method, exact solution is not reached in every run. Though the suboptimal solution obtained is very near to the exact one. Computational result comprising an average performance is also presented here.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.8 no.4
• /
• pp.38-44
• /
• 1999

This paper primarily directed toward analyzing the frequency response in hydraulic pipe lines with a small diameter. The exact solution to the frequency response is obtained by using the complicated transfer function. The discrepancy with the exact and the approximate is small so the approximation solution is adopted to compare the experimental results with the theoretical analysis. In this experiment the input frequency was generated by the frequency generator with the ball valve and speed controller. In order to compare the theoretical were forms with the experimental ones the trace obtained from the oscilloscope is photographed, The diameter the length of lines and input pressure amplitude are varied to investigate their effects,. the experiment results show that th values of dimensionless parameter are very affected to the phase delay and guide response time in the design of pressure manifold to measure the pressure of hydraulic pipelines.

• Proceedings of the KSME Conference
• /
• 2001.06e
• /
• pp.760-765
• /
• 2001

Some multidimentional generalizations of the Fokker-Planck Equation used by Friedrich and Peinke for description of a turbulent cascade was solved by A.A.Donkov, A.D.Donkov, and G.I.Grancharova. The solutions are two types, isotropic and anisotropic diffusion case. We introduce their methods to solve the Equation and solutions. Furthermore we get the more generalized exact solution as combination of two cases and plot to compare those to experimental results for the isotropic case.

• Journal of Advanced Marine Engineering and Technology
• /
• v.8 no.1
• /
• pp.100-111
• /
• 1984

The methods solving the 2nd order linear ordinary differential equations of the form y"+H(x)y'+G(x)y=P(x) using Fourier series are presented in this paper. These methods are applied to the differential equations of which the exact solutions are known, and the solutions by Fourier series are compared with the exact solutions. The main results obtained in these studies are summarized as follows; 1) The product and the quotient of two functions expressed in Fourier series can be expressed also in Fourier series and the relations between the Fourier coefficients of the series are obtained by multiplying term by term. 2) If the solution of the 2nd order lindar ordinary differential equation exists in a certain interval, the solution can be obtained using Fourier series and can be expressed in Fourier series. 3) The absolute errors of Fourier series solutions are generally less in the center of the interval than in the end of the interval. 4) The more terms are considered in Fourier series solutions, the less the absolute errors.rors.

• Journal of applied mathematics & informatics
• /
• v.27 no.1_2
• /
• pp.441-452
• /
• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.