• 대한수학회보
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• 제43권2호
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• pp.253-263
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• 2006

In this paper we introduce a new concept, a 'periodicizing' function for the linear differential equation with the periodic forcing function. Moreover, we construct this function, which is closely related with the solution of a difference equation and an indefinite sum. Using this function, we can obtain a representation of solutions from which we see immediately the asymptotic behavior of the solutions.

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.271-283
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• 2018

In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.

• 대한수학회보
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• 제61권3호
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• pp.745-762
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• 2024

In this paper, we study the existence of finite order meromorphic solutions of the following non-linear difference equation fⁿ(z) + P_d(z, f) = p₁e^α1z + p₂e^α2z + p₃e^α3z, where n ≥ 2 is an integer, P_d(z, f) is a difference polynomial in f of degree d ≤ n - 2 with small functions of f as its coefficients, p_j (j = 1, 2, 3) are small meromorphic functions of f and α_j (j = 1, 2, 3) are three distinct non-zero constants. We give the expressions of finite order meromorphic solutions of the above equation under some restrictions on α_j (j = 1, 2, 3). Some examples are given to illustrate the accuracy of the conditions.

• 대한수학회보
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• 제55권6호
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• pp.1755-1771
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• 2018

In this paper, we investigate a certain type of q-difference Riccati equation in the complex plane. We prove that q-difference Riccati equation possesses a one parameter family of meromorphic solutions if it has three distinct meromorphic solutions. Furthermore, we find that all meromorphic solutions of q-difference Riccati equation and corresponding second order linear q-difference equation can be expressed by q-gamma function if this q-difference Riccati equation admits two distinct rational solutions and $q{\in}{\mathbb{C}}$ such that 0 < ${\mid}q{\mid}$ < 1. The growth and value distribution of differences of meromorphic solutions of q-difference Riccati equation are also treated.

• 대한수학회지
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• 제36권5호
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• pp.833-846
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• 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
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• 제13권1_2호
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• pp.11-27
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• 2003

A fourth order in time and second order in space scheme using a finite-difference method is developed for the non-linear Boussinesq equation. For the solution of the resulting non-linear system a predictor-corrector pair is proposed. The method is analyzed for local truncation error and stability. The results of a number of numerical experiments for both the single and the double-soliton waves are given.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.473-481
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• 2021

In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic coefficients of finite logarithmic order. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.

• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.237-243
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• 2024

A similarity transformation of a solution of the Cauchy problem for the linear difference equation in Hilbert space has been studied. In this manuscript, we obtain necessary and sufficient conditions for linear equivalence of the discrete semigroup of operators, generated by the solution of the difference equation utilizing four Canonical semigroups.

• 조명전기설비학회논문지
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• 제18권4호
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• pp.68-72
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• 2004

본 논문에서는 선형 액추에이터의 권선부에 구형파 전압을 인가시 권선부의 표면에 나타나는 온도의 변화에 대해서 고찰하였다. 또한 테일러급수로부터 구할 수 있는 유한차분 방정식을 유도하였고, 이를 바탕으로 직선형 피스톤 액추에이터의 권선에서 일어나는 온도 변화에 대한결과를 고찰하였다. 그 결과 액추에이터 표면의 온도가 주위온도에 비해 시간에 따라 증가하는 에너지 표출 현상을 확인하였으며 이를 바탕으로 선형 액추에이터의 동작시 온도 특성을 실제 시스템에 고려하여 적용할 수 있는 실험적 자료를 도출할 수 있었다. 이에 관한 결과는 액추에이터 뿐만 아니라 권선을 사용하는 전동기나 변압기와 같은 전기기기와 전자기력을 이용하는 분야에 참고자료로 활용될 수 있으리라 사료되며, 앞으로는 여러 조건 하에서 권선의 내부와 외부에서 일어나는 온도 및 동작 특성의 정밀한 해석 결과를 구하기 위해 좀더 구체적인 계산 방범과 개선이 필요하다.

• Journal of applied mathematics & informatics
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• 제41권1호
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• pp.167-179
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• 2023

In this paper, we investigate solutions of equations which are linear (p, q)-difference equation of higher order by using (p, q)-derivative and integral. We also derive the solution of equation in the case of second order.