• Journal of information and communication convergence engineering
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• v.10 no.1
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• pp.66-70
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• 2012

Conformal mapping has been a familiar tool of science and engineering for generations. Determination of a conformal map from the unit disk onto the Jordan region is reduced to solving the Theodorsen equation, which is an integral equation for boundary correspondence functions. There are many methods for solving the Theodorsen equation. It is the goal of numerical conformal mapping to find methods that are at once fast, accurate, and reliable. In this paper, we analyze Niethammer’s solution based on successive over-relaxation (SOR) iteration and Wegmann’s solution based on Newton iteration, and compare them to determine which one is more effective. Through several numerical experiments with these two methods, we can see that Niethammer’s method is more effective than Wegmann’s when the degree of the problem is low and Wegmann’s method is more effective than Niethammer’s when the degree of the problem is high.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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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 The Korean Society of Agricultural Engineers
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• v.65 no.2
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• pp.35-45
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• 2023

The DOR (Drainage outlet raising) in the paddy field has been suggested as one of the most important best management practices for the TMDL (Total maximum daily load) management in the technical guidelines by the NIER (National institute of environmental research). However, this method is underestimated and is not well adopted by local governments for the TMDL. The purpose of this study is to evaluate the unit load reduction equation according to the application of DOR in order to expand this equation. The original equation in the guideline was derived using the HSPF (Hydrological Simulation Program-Fortran) model for 1 year in Changnyeong. We analyzed the reduction effect of the original equation application by collecting additional long-term monitoring data from the Buan, Icheon, Iksan, and Jeonju. When comparing the reduction loads between the original equation and monitoring results, the evaluation results of the original equation were 11% of the monitoring analysis results, which was underestimated. This means that the original equation needs to be improved. For assessing the equation, the HSPF Paddy-RCH model was established according to the NI ER guideline and evaluated for applicability. The performance results of the model showed a reasonable range by the statistical criteria. Modified equations 1 and 2 were proposed based on the monitoring and modeling results. Modified equation 1 was the method of modifying the original equation's main factors, and modified equation 2 was the method of applying the non-point pollution reduction efficiency according to the rainfall class using the long-term modeling results. At the level of 58.6~64.6% of monitoring data, the difference between them could be further reduced compared to the original equation. The suggested approach will be more reasonable and practicable for decision-makers and will contribute to the TMDL management plans.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.611-624
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• 2010

A Numerical scheme based on collocation method using quartic B-spline functions is designed for the numerical solution of one-dimensional modified equal width wave (MEW) wave equation. Using Von-Neumann approach the scheme is shown to be unconditionally stable. Performance of the method is validated through test problems including single wave, interaction of two waves and use of Maxwellian initial condition. Using error norms $L_2$ and $L_{\infty}$ and conservative properties of mass, momentum and energy, accuracy and efficiency of the suggested method is established through comparison with the existing numerical techniques.

• Bulletin of the Society of Naval Architects of Korea
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• v.19 no.4
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• pp.19-29
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• 1982

Galerkin's finite element method is applied to a two-dimensional heat convection-diffusion problem arising in the hydrodynamic lubrication of thrust bearings used in naval vessels. A parabolized thermal energy equation for the lubricant, and thermal diffusion equations for both bearing pad and the collar are treated together, with proper juncture conditions on the interface boundaries. it has been known that a numerical instability arises when the classical Galerkin's method, which is equivalent to a centered difference approximation, is applied to a parabolic-type partial differential equation. Probably the simplest remedy for this instability is to use a one-sided finite difference formula for the first derivative term in the finite difference method. However, in the present coupled heat convection-diffusion problem in which the governing equation is parabolized in a subdomain(Lubricant), uniformly stable numerical solutions for a wide range of the Peclet number are obtained in the numerical test based on Galerkin's classical finite element method. In the present numerical convergence errors in several error norms are presented in the first model problem. Additional numerical results for a more realistic bearing lubrication problem are presented for a second numerical model.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.3
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• pp.101-107
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• 1990

In this work, one-dimensional simulation is carried out for PT-GaAs Schottky barrier diodes with finite difference method. Shockley's semiconductor governing equations: Poisson equation and current continuity equation are discertized, and linearized by Newton-Raphson method. The linear system of equation is solved by Gaussian elimination method until convergence is achieved. The boundary condition for this equation is taken from thermionic emission-diffusion theory. Simulation is done for PT-GaAs epitaxial-layer Schottky barrier diodes. The claculated results of electron and potential distribution are shown. Simulation results show exellent agreement with experiments.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.517-527
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• 2016

In this paper, we consider a thermoviscoelastic equation which has one end fixed and output feedback control at the other end. We prove the existence of solutions using the Galerkin method and then investigate the exponential stability of solutions by using multiplier technique.

• Journal of Korean Association for Spatial Structures
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• v.2 no.1 s.3
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• pp.75-84
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• 2002

In this study, the 'force density method' for shape finding of cable net structures is presented. This concept is based on the force-length ratios or force densities which are defined for each branch of the net structures. This method renders a simple linear 'analytical form finding' possible. If the free choice of the force densities is restricted by further condition, the linear method is extended to a nonlinear one. The nonlinear one can be applied to the detailed computation of networks. In this paper, the general inverse matrix is introduced to solve the nonlinear equilibrium equation including Jacobian matrix which is rectangular matrix. Several examples for linear and nonlinear analysis applied additional constraints are presented. It is shown that the force density method is suitable for form finding of cable net and the general inverse matrix can be applied to solve the nonlinear equation without Lagrangian factors.

• Nuclear Engineering and Technology
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• v.22 no.2
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• pp.151-158
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• 1990

The new discrete elements method (DEM) is applied to the one-group neutron transport equation in one-dimensional slab geometry. The fixed source and the criticality problems are treated and three spatial differencing schemes (the DD, the SC, -and the LC schemes) are tested to determine the most computationally efficient in the DEM. In all cases, the accuracy of the results obtained from the DEM shows an improvement over that obtained from the standard discrete ordinates calculations. And the LC scheme gives the most accurate results in the DEM.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.411-423
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• 2010

In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.