• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.609-621
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• 2013

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.7
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• pp.586-591
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• 2007

The effects of cancellation errors on the convergence characteristics of preconditioned Euler equations at low Mach numbers are analyzed. Flows in a two-dimensional channel with a circular bump are calculated at different Mach numbers. It is shown that the cancellation error in the energy equation grows faster than those in the other equations as the Mach number decreases. It is also shown that the cancellation problem of the energy equation can be alleviated by multiplying the inversion of the preconditioner.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.25 no.10
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• pp.1077-1086
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• 2014

We propose a design method of a Rotman lens for curved array antenna applicable to conformal array. In this paper, design equations are derived to obtain an array curve, transmission line lengths of a Rotman lens in conjunction with a curved array antenna, and the phase error of a Rotman lens based on these design equations is minimized through the beam curve optimization procedure and the refocusing procedure. Rotman lenses designed by the proposed design equations and design procedures still maintain 3 focal points, can feed a convex or concave array antenna with circular curve, parabolic curve, V-shaped curve, etc as well as a straight line array antenna, and have minimal phase error.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.123-131
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• 2006

In this paper, a numerical programming for Liapunov index of differential equations with periodic coefficients depending on parameters is given. The associated equations are given at first, then existence of periodic solutions to the associated equations is proved in this paper. And we compute periodic solution u(t) of the associated equations. Finally, we give the error of approximate calculation.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.317-332
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• 2005

In this paper we consider the hp-version to solve non-constant coefficients elliptic equations on a bounded, convex polygonal domain ${\Omega}$ in $R^2$. A family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties can be used for calculating the integrals. When the numerical quadrature rules $I_m{\in}G_p$ are used for computing the integrals in the stiffness matrix of the variational form we will give its variational form and derive an error estimate of ${\parallel}u-{\widetilde{u}}^h_p{\parallel}_{1,{\Omega}$.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.299-306
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• 2008

Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations, which discribe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^\infty$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1725-1739
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• 2016

Abstract. Numerical solutions for the evolutionary space fractional order differential equations are considered. A predictor corrector method is applied in order to obtain numerical solutions for the equation without solving nonlinear systems iteratively at every time step. Theoretical error estimates are performed and computational results are given to show the theoretical results.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.113-122
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• 2005

We consider the iterative schemes for the large sparse linear system to solve partial differential equations. Using spectral radius of iteration matrices, the optimal relaxation parameters and good parameters can be obtained. With those parameters we compare the effectiveness of the SOR and SSOR algorithms. Applying Crank-Nicolson approximation, we observe the error distribution according to domain decomposition. The number of processors due to domain decomposition affects time and error. Numerical experiments show that effectiveness of SOR and SSOR can be reversed as time size varies, which is not the usual case. Finally, these phenomena suggest conjectures about equilibrium time grid for SOR and SSOR.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.223-235
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• 2006

By applying the Landau-type transformation, we transform a Stefan problem with nonlinear free boundary condition into a system consisting of a parabolic equation and the ordinary differential equations. Fully discrete finite element method is developed to approximate the solution of a system of a parabolic equation and the ordinary differential equations. We derive optimal orders of convergence of fully discrete approximations in $L_2,\;H^1$ and $H^2$ normed spaces.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.515-531
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• 1997

In this paper, finite difference method is applied to approximate the generalized solutions of Sobolev equations. Using the Steklov mollifier and Bramble-Hilbert Lemma, a priori error estimates in discrete $L^2$ as well as in discrete $H^1$ norms are derived frist for the semidiscrete methods. For the fully discrete schemes, both backward Euler and Crank-Nicolson methods are discussed and related error analyses are also presented.