• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.265-277
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• 2004

This article deals with the number of periodic solutions of the second order polynomial differential equation using the Riccati equation, and applies the property of the solutions of the Riccati equation to study the property of the solutions of the more complicated differential equations. Many valuable criterions are obtained to determine the number of the periodic solutions of these complex differential equations.

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.329-342
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• 2002

We deal with asymptotic properties of Maximum Likelihood Estimator(MLE) for the parameters appearing in a Hilbert space-valued Stochastic Differential Equation(SDE) and a Stochastic Partial Differential Equation(SPDE). In paractice, the available data are only the finite dimensional projections to the solution of the equation. Using these data we obtain MLE and consider the asymptotic properties as the dimension of projections increases. In particular we explore a relationship between the conditions for the solution and asymptotic properties of MLE.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.383-388
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• 1991

This paper analizes two numerical integration methods, both based on the Runge Kutta 4-th order formula for deterministic systems, for digital simulation of a differential equation driven by white noise. It is shown that a "standard' Runge Kutta method for stochasitic systems yields solutions of Stratonovich differential equations, while Riggs and Phillips' method results in solutions of Ito differential equations. Therefore the white noise differential equation must be converted into the equivalent Ito equation before the latter method is used. Digital simulation results for a simple differential equation are also presented.nted.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.171-177
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• 2018

In this research paper considering a differential equation with impulsive effect and dependent delay and applied Banach fixed point theorem using the impulsive condition to the impulsive fractional functional differential equation of an order ${\alpha}{\in}(1,2)$ to get an uniqueness solution. At last, theorem is verified by using a numerical example to illustrate the uniqueness solution.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.71-82
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• 2023

In this article, we find the approximate solutions of Abel differential equation (ADE) with uncertainty using residual power series (RPS) method. This method helps to calculate the sequence of solutions of ADE. Finally, numerical illustrations demonstrate the applicability of the method.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.47-60
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• 1997

In the theory of the conditional Wiener integral, the integrand is a functional of the standard Wiener process. In this paper we consider a conditional function space integral for functionals of more general stochastic process and the generalized Kac-Feynman integral equation. We first show that the existence of a partial differential equation. We then show that the generalized Kac-Feynman integral equation is equivalent to the partial differential equation.

• Industrial Engineering and Management Systems
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• v.12 no.1
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• pp.2-8
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• 2013

Uncertainty theory is a branch of mathematics based on normolity, duality, subadditivity and product axioms. Uncertain process is a sequence of uncertain variables indexed by time. Canonical Liu process is an uncertain process with stationary and independent increments. And the increments follow normal uncertainty distributions. Uncertain differential equation is a type of differential equation driven by the canonical Liu process. Stability analysis on uncertain differential equation is to investigate the qualitative properties, which is significant both in theory and application for uncertain differential equations. This paper aims to study stability properties of linear uncertain differential equations. First, the stability concepts are introduced. And then, several sufficient and necessary conditions of stability for linear uncertain differential equations are proposed. Besides, some examples are discussed.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.161-173
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• 1996

When we deal with a Hilbert space-valued Stochastic Differential Equation (SDE) (or Stochastic Partial Differential Equation (SPDE)), depending on some unknown parameters, the solution usually has a Fourier series expansion. In this situation we consider the maximum likelihood method for the statistical estimation problem and derive the asymptotic properties (consistency and normality) of the Maximum Likelihood Estimator (MLE).

• Journal of Environmental Impact Assessment
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• v.10 no.4
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• pp.319-326
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• 2001

This study is aimed at the development of a comprehensive web-based partial differential equation solver (WPDES) using multidimensional finite element method, which can be operated on the basis of world wide web. Overall issues of engineering and environmental information management and facility control could be implemented using this solver. This paper describes the development technique of the model, which is first part on development of partial differential equation solver. Conventional commercial general solver of computational fluid dynamics problems were investigated. All the relevant environmental models were analyzed to develop integrated environmental management system using WPDES. The governing equations and the parameters of investigated models were analyzed and integrated. Several numerical modules were invented for each partial differential term in partial differential equation of many related modeling problems. Each module was coded in the fashion of object oriented method, and was combined independently for the overall governing equation. WPDES has unique characteristic, which can analyze the problem through the suitable combination of modules without development of additional models for each environment problem with different governing equation, main variables, and parameters.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.319-328
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• 2004

In this paper we investigate the qualitative behaviour of numerical approximation to a class delay differential equation. We consider the numerical solution of the delay differential equations undergoing a Hopf bifurcation. We prove the numerical approximation of delay differential equation had a Hopf bifurcation point if the true solution does.