• Journal of the Korean Mathematical Society
• /
• v.36 no.5
• /
• pp.833-846
• /
• 1999

In this paper, we will study the relationship between the controlling factor of the solution to a difference equation and the solution of the corresponding differential equation. Many times the controlling factors are the same. But even the controlling factor of the two solutions may be different, we will discover a way to compute, for first order non-linear equations, the controlling factor of the solution to the difference equation using the solution of the differential equation.

• Journal of applied mathematics & informatics
• /
• v.35 no.3_4
• /
• pp.277-302
• /
• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.4
• /
• pp.635-644
• /
• 2010

We investigate the boundedness and asymptotic almost periodicity of solutions for discrete Volterra equations.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.3
• /
• pp.413-426
• /
• 2008

An asymptotic solution of a fourth order critically damped nonlinear differential system has been found by means of extended Krylov-Bogoliubov-Mitropolskii (KBM) method. The solutions obtained by this method agree with those obtained by numerical method. The method is illustrated by an example.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.6
• /
• pp.1255-1262
• /
• 2012

A type of delayed Lotka-Volterra competition reaction-diffusion system is considered. By constructing a new Lyapunov function, we prove that the unique positive steady-state solution is globally asymptotically stable when interspecies competition is weaker than intraspecies competition. Moreover, we show that the stability property does not depend on the diffusion coefficients and time delays.

• 제어로봇시스템학회:학술대회논문집
• /
• 1990.10a
• /
• pp.519-522
• /
• 1990

This paper formulates a problem of analysis and design of serial production lines, closed with respect to the number of carriers available in the system for parts transportation between operations. For two machines - two buffers systems, the paper gives an asymptotic solution and shows that optimization of the system with respect to the number of carriers available and the capacity of the feedback buffer may lead to substantial improvements of system's performance.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.663-675
• /
• 2007

We investigate the representation of the solution of discrete linear Volterra difference systems by means of the resolvent matrix and fundamental matrix, respectively, and then study the boundedness of the solutions of discrete Volterra systems by improving the assumptions and the proofs of Medina#s results in [6].

• Communications of the Korean Mathematical Society
• /
• v.24 no.1
• /
• pp.85-97
• /
• 2009

In this paper we study the existence of global weak solutions for a hyperbolic hemivariational inequalities with boundary source and damping terms, and then investigate the asymptotic stability of the solutions by using Nakao Lemma [8].

• Journal of applied mathematics & informatics
• /
• v.9 no.1
• /
• pp.261-275
• /
• 2002

Besides asymptotic method, the method of orthogonal polynomials has been used to obtain the solution of the Fredholm integral equation. The principal (singular) part of the kerne1 which corresponds to the selected domain of parameter variation is isolated. The unknown and known functions are expanded in a Chebyshev polynomial and an infinite a1gebraic system is obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.21 no.4
• /
• pp.203-214
• /
• 2017

In this paper we propose and analyze two a posteriori error estimators for the stabilized $P_1/P_1$ finite element discretization of the Stokes equations. These error estimators are computed by solving local Poisson or Stokes problems on elements of the underlying triangulation. We establish their asymptotic exactness with respect to the velocity error under certain conditions on the triangulation and the regularity of the exact solution.