• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.683-691
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• 2001

A linearized finite-difference scheme is used to transform the initial/boundary-value problem associated with the nonlinear Schrodinger equation into a linear algebraic system. This method is developed by replacing the time and the nonlinear term by an appropriate parametric linearized scheme based on Taylor’s expansion. The resulting finite-difference method is analysed for stability and convergence. The results of a number of numerical experiments for the single-soliton wave are given.

• Journal of Korean Society of Forest Science
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• v.90 no.2
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• pp.210-216
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• 2001

Pinus densiflora S. et Z. has widely been distributed, and is one of the important main foret resources in Korea. Diameter and height growth patterns were estimated using non-linear algebraic difference equation, which requires two-measurement times $T_1$ and $T_2$. To maximize data use, all possible measurement interval data were derived using Lag and Put statements in the SAS. In results, of the algebraic difference equations applied, the Schumacher and the Gompertz polymorphic equations for diameter and height, respectively showed the higher precision of the fitting. In order to allow more precise estimation of growth than those of the basic Schumacher and the Gompertz, further refinement that combine biological realism as input into the equation would be necessary.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.23-26
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• 2002

An evaluation of one algebraic and two one-equation eddy viscosity-transport turbulence closure models as implemented to the CFDS(Characteristic Flux Difference Splitting) scheme is presented for the efficient computation of the turbulent flow. Comparisons of Baldwin-Lomax model as algebraic turbulence model and Baldwin-Barth and Spalart-Allmaras model as one-equation turbulence model are presented for three test cases for 3-dimensional flow. The numerical result of the CFDS schem is examined through comparison with the experimental data.

• Coupled systems mechanics
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• v.8 no.2
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• pp.129-146
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• 2019

The main goal of this work is to develop a numerical simulator to study an isothermal single-phase two-component flow in a naturally fractured oil reservoir, taking into account advection and diffusion effects. We use the Peng-Robinson equation of state with a volume translation to evaluate the properties of the components, and the discretization of the governing partial differential equations is carried out using the Finite Difference Method, along with implicit and first-order upwind schemes. This process leads to a coupled non-linear algebraic system for the unknowns pressure and molar fractions. After a linearization and the use of an operator splitting, the Conjugate Gradient and Bi-conjugated Gradient Stabilized methods are then used to solve two algebraic subsystems, one for the pressure and another for the molar fraction. We studied the effects of fractures in both the flow field and mass transport, as well as in computing time, and the results show that the fractures affect, as expected, the flow creating a thin preferential path for the mass transport.

• Bulletin of the Society of Naval Architects of Korea
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• v.13 no.1
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• pp.17-23
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• 1976

Some methods of analysis of rectangular plates under distributed load of various intensity with interior supports are presented herein. Analysis of many structures such as bottom, side shell, and deck plate of ship hull and flat slab, with or without internal supports, Floor systems of bridges, included crthotropic bridges is a problem of plate with elastic supports or continuous edges. When the four edges of rectangular plate is simply supported, the double Fourier series solution developed by Navier can represent an exact result of this problem. If two opposite edges are simply supported, Levy's method is available to give an "exact" solution. When the loading condition and supporting condition of a plate does not fall into these cases, no simple analytic method seems to be feasible. Analysis of a simply supported rectangular plate under irregularly distributed loads of various intensity with internal supports is carried out by applying Navier solution well as the "Principle of Superposition." Finite difference technique is used to solve plates under irregularly distributed loads of various intensity with internal supports and with various boundary conditions. When finite difference technique is applied to the Lagrange's plate bending equation, any of fourth order derivative term in this equation produces at least five pivotal points leading to some troubles when the resulting linear algebraic equations are to be solved. This problem was solved by reducing the order of the derivatives to two: the fourth order partial differential equation with one dependent variable, namely deflection, is changed to an equivalent pair of second order partial differential equations with two dependent variables. Finite difference technique is then applied to transform these equations to a set of simultaneous linear algebraic equations. Principle of Superposition is then applied to handle the problems caused by concentrated loads and interior supports. This method can be used for the cases of plates under irregularly distributed loads of various intensity with arbitrary conditions such as elastic supports, or continuous edges with or without interior supports, and this method can also be solve the influence values of deflection, moment and etc. at arbitrary position of plates under the live load.

• Journal of Korean Society of Forest Science
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• v.89 no.4
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• pp.463-469
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• 2000

Douglas-fir (Pseudotsuga menziesd Mirb. Franco) is highly regarded as a commercial timber species throughout the world in part due to its fast growth relative to many other species. In this study, basal area per hectare equation for Douglas-fir plantations in Southland of New Zealand has been developed based on medium measurement cycles of permanent sample plots data set. The function was developed using the algebraic difference equation method, and various sigmoid-shaped projection equations were used. Parameter estimation was obtained by non-linear routine of the SAS. As a result, of the functions tested a variant of the Schumacher polymorphic function including site index and thinning term as predictor variables showed the higher precision of the fitting. The results indicate that site index is positively correlated with basal area growth. And the thinning term was found to be useful to increase precision of the model.

• East Asian mathematical journal
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• v.33 no.1
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• pp.53-65
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• 2017

Numerical solutions of the Rosenau-Burgers equation based on the cubic B-spline finite element method are introduced. The backward Euler method is used for discretization in time, and the obtained nonlinear algebraic system is changed to a linear system by the Newton's method. We show that those methods are unconditionally stable. Two test problems are studied to demonstrate the accuracy of the proposed method. The computational results indicate that numerical solutions are in good agreement with exact solutions.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.185-196
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• 1988

We study existence of polynomial integrating factors and solutions F(x, y)=c of first order nonlinear differential equations. We characterize the homogeneous case, and give algorithms for finding existence of and a basis for polynomial solutions of linear difference and differential equations and rational solutions or linear differential equations with polynomial coefficients. We relate singularities to nature of the solution. Solution of differential equations in closed form to some degree might be called more an art than a science: The investigator can try a number of methods and for a number of classes of equations these methods always work. In particular integrating factors are tricky to find. An analogous but simpler situation exists for integrating inclosed form, where for instance there exists a criterion for when an exponential integral can be found in closed form. In this paper we make a beginning in several directions on these problems, for 2 variable ordinary differential equations. The case of exact differentials reduces immediately to quadrature. The next step is perhaps that of a polynomial integrating factor, our main study. Here we are able to provide necessary conditions based on related homogeneous equations which probably suffice to decide existence in most cases. As part of our investigations we provide complete algorithms for existence of and finding a basis for polynomial solutions of linear differential and difference equations with polynomial coefficients, also rational solutions for such differential equations. Our goal would be a method for decidability of whether any differential equation Mdx+Mdy=0 with polynomial M, N has algebraic solutions(or an undecidability proof). We reduce the question of all solutions algebraic to singularities but have not yet found a definite procedure to find their type. We begin with general results on the set of all polynomial solutions and integrating factors. Consider a differential equation Mdx+Ndy where M, N are nonreal polynomials in x, y with no common factor. When does there exist an integrating factor u which is (i) polynomial (ii) rational? In case (i) the solution F(x, y)=c will be a polynomial. We assume all functions here are complex analytic polynomial in some open set.

• Journal of Korean Society of Transportation
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• v.13 no.2
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• pp.43-58
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• 1995

This paper discusses some of the results of investigation of railroad-highway grade crossing accidents and accident-related inventory information that was collected from the Pusan District Office of the Korean National Railroads. Established statistical techniques were applied to tabulated data to obtain an accident prediction equation that estimates the expected probability of accidents at each crossing under various grade crossing situations. It was found that the most significant factor that influences the railroad crossing accidents was flagger. The other factors were train and traffic volumes, number of tracks. crossing angle, maximum timetable train speed, algebraic grade difference, and lighting facility. No significant effects was identified with railroad crossing gates. The results of the analysis and the uses of the prediction equation for the development of warrants for safety improvements are also discussed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.11a
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• pp.474-478
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• 2008

In this paper, the technique to reinforce the structure using the sensitivity information is proposed. Design variables related to the geometry of structure at fatigue fracture points are determined and sensitivities of fatigue life at fracture points with respect to the variation of design variables are calculated. Then the vector composed of gaps between the target life and initial life cycles at fracture points is calculated. The linear algebraic equation to solve the variation of design variables is composed. From the equation, the design variables for reinforced structure are determined.