• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.57-69
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• 2012

In this paper, we prove the existence of mild solutions for a first order impulsive neutral differential inclusion with state dependent delay. We assume that the state-dependent delay part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multi-valued maps, a main existence theorem is established.

• ETRI Journal
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• v.23 no.2
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• pp.71-76
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• 2001

In this paper, the electromagnetic characteristics of a grounded slab and a parallel-plate structure are analyzed by the Spline-type Divided-Difference Interpolation (SDDI) technique. The technique efficiently evaluates the MoM impedance matrix elements of the multifold spectral or spatial domain integrals or summation in integro differential equations. The numerical results of the proposed method agree well with those of the corresponding literatures.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.681-696
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• 2011

In this paper, we consider the existence of mild solutions for a certain class of nonlinear impulsive functional evolution integrodifferential equation with nonlocal conditions in Banach spaces. A sufficient condition is established by using Schaefer's fixed point theorem combined with an evolution system. An example is also given to illustrate our result.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.161-176
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• 2005

We consider a model of population dynamics whose mortality function is unbounded. We note that the regularity of the solution depends on the growth rate of the mortality near the maximum age. We propose Gauss-Legendre methods along the characteristics to approximate the solution when the solution is smooth enough. It is proven that the scheme is convergent at fourth-order rate in the maximum norm. We also propose discontinuous Galerkin finite element methods to approximate the solution which is not smooth enough. The stability of the method is discussed. Several numerical examples are presented.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.623-640
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• 2007

The Lotka-McKendrick model which describes the evolution of a single population is developed from the well known Malthus model. In this paper, we introduce the Lotka-McKendrick model. We approximate the solution to the model using hp-discontinuous Galerkin finite element method. The numerical results show that the presented hp-discontinuous Galerkin method is very efficient in case that the solution has a sharp decay.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.559-569
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• 2013

The purpose of this paper is to establish existence, uniqueness and a variation of constant formula of solutions for semilinear partial functional differential equations with unbounded delays and nonlinear part involving integro differetial terms.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.503-508
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• 2016

We propose a number of finite difference methods for the prices of a European option under the CGMY model. These numerical methods to solve a partial integro-differential equation (PIDE) are based on three time levels in order to avoid fixed point iterations arising from an integral operator. Numerical simulations are carried out to compare these methods with each other for pricing the European option under the CGMY model.

• Proceedings of the KIEE Conference
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• 1995.07a
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• pp.53-55
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• 1995

This paper presents the characteristics of linear induction motors fed by a voltage source PWM inverter. In the calculation, 2D finite element method is used considering the movement by moving mesh. Integro-differential approach is adopted for the copper loss calculation considering the skin effect.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.1 no.1
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• pp.83-104
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• 1997

This paper studies parameter estimation for a first-order hyperbolic integro-differential equation modelling one-sex population dynamics. A second-order finite difference scheme is used to estimate parameters such as the age-specific death-rate and the age-specific fertility from fully discrete observations on the population. The function space parameter estimation convergence of this scheme is proved. Also, numerical simulations are performed.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.767-779
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• 2003

We consider a model of population dynamics whose mortality function is unbounded. We approximate the solution of the model using a discontinuous Galerkin finite element for the age variable and a backward Euler for the time variable. We present several numerical examples. It is experimentally shown that the scheme converges at the rate of $h^{3/2}$ in the case of piecewise linear polynomial space.