• Communications of Mathematical Education
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• v.28 no.3
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• pp.339-352
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• 2014

In this paper we introduce mathematical modellings in teaching and learning differential equations which were adopted by 2009 revised curriculum. The textbook of 'Advanced Mathematics II' published in 2014 with one publisher includes the content of the second order differential equation y"+y=0 by the power series method. This paper discusses the issue of the power series and gives an alternative method to explain problems of differential equation. Also, we found that the textbook of 'Advanced Mathematics II' used the mechanical system not electrical system in solving differential equation problems. Thus this paper suggests a method using an electric circuit in teaching and learning the first order differential equation. Finally we suggest some terminologies in the teaching and learning of differential equations.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.763-779
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• 2011

In this paper we apply the Exp-function method to obtain traveling wave solutions of three nonlinear partial differential equations, namely, generalized sinh-Gordon equation, generalized form of the famous sinh-Gordon equation, and double combined sinh-cosh-Gordon equation. These equations play a very important role in mathematical physics and engineering sciences. The Exp-Function method changes the problem from solving nonlinear partial differential equations to solving a ordinary differential equation. Mainly we try to present an application of Exp-function method taking to consideration rectifying a commonly occurring errors during some of recent works.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.791-804
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• 2006

This paper is concerned with a second-order iterated differential equation of the form $c_0x'(Z)+c_1x'(z)+c_2x(z)=x(az+bx(z))+h(z)$ with the distinctive feature that the argument of the unknown function depends on the state. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.225-236
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• 2002

By means of the method of majorant series, sufficient conditions are obtained for the existence of analytic solutions of a functional differential equation with proportional delays.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.337-346
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• 2016

Within white noise approach, we study the existence and uniqueness of the solution of an initial value problem for generalized white noise functionals, and then as a corollary we discuss the linear stochastic differential equation associated with a convolution of white noise functionals.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2001-2010
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• 2015

In this paper, we give explicit and new identities for the Bernoulli numbers of the second kind which are derived from a non-linear differential equation.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.267-275
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• 2021

In this study, we investigate the generalized Hyers-Ulam Stability of partial differential equation of the form y_t - ky_xx = 0.

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.901-903
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• 1995

The ordinary differential equation (ODE) method has been widely used for the convergence analysis of stochastic recursive algorithms. The principal objective of this method is to associate to a given algorithm a differential equation with continuous righthand side. Usually some assumptions should be imposed to get such a differential equation. If any of assumptions fails, then the ODE method cannot be used. Recently a new method using differential inclusions (DIs) was introduced in [3], which is useful to deal with those cases. The DI method shares the same idea with the ODE method, but it is different in that a differential inclusion is identified instead of a differential equation with continuous righthand side. In this paper, we briefly review the DI method and then analyze a Robbins and Monro (RM)-type algorithm. Our focus is placed on the projected algorithm.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.509-517
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• 2005

We shall prove the existence and uniqueness theorem of a solution to the non local fuzzy differential equation using the contraction mapping principle.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.445-454
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• 2011

In this paper, we first find a raising operator and a lowering operator for multiple Bessel polynomials and then give a differential equation having multiple Bessel polynomials as solutions. Thus the differential equations were found for all multiple orthogonal polynomials that are orthogonal with respect to the same type of classical weights introduced by Aptekarev et al.