• Korean Journal of Mathematics
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• 제13권1호
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• pp.113-122
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• 2005

We consider the iterative schemes for the large sparse linear system to solve partial differential equations. Using spectral radius of iteration matrices, the optimal relaxation parameters and good parameters can be obtained. With those parameters we compare the effectiveness of the SOR and SSOR algorithms. Applying Crank-Nicolson approximation, we observe the error distribution according to domain decomposition. The number of processors due to domain decomposition affects time and error. Numerical experiments show that effectiveness of SOR and SSOR can be reversed as time size varies, which is not the usual case. Finally, these phenomena suggest conjectures about equilibrium time grid for SOR and SSOR.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.723-736
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• 2016

This paper shows that the solutions to nonlinear perturbed differential system $$y^{\prime}= f(t,y)+{\int_{t_{0}}^{t}g(s,y(s))ds+h(t,y(t),Ty(t))$$ have bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_{0}}^{t}g(s,y(s))ds,\;h(t, y(t),\;Ty(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of h-stability.

• 대한수학회보
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• 제32권1호
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• pp.13-18
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• 1995

In order to investigate the differential structure of a Riemannian manifold (M, g), it seems a powerful tool to study the differential structure of its tangent bundle TM. In this point of view, K. Aso [1] studied, using the Sasaki metric $\tilde{g}$, the relation between the curvature tensor on (M, g) and that on (TM, $\tilde{g}$).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권4호
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• pp.335-354
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• 2007

In this paper, we define an analogue of generalized Wiener measure and investigate its basic properties. We define (${\hat}It{o}$ type) stochastic integrals with respect to the generalized Wiener process and prove the ${\hat}It{o}$ formula. The existence and uniqueness of the solution of stochastic differential equation associated with the generalized Wiener process is proved. Finally, we generalize the linear filtering theory of Kalman-Bucy to the case of a generalized Wiener process.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권2호
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• pp.171-177
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• 2012

The main purpose of this paper is to investigate $h$-stability of the nonlinear perturbed differential systems using the notion of $t_{\infty}$-similarity. As results, we generalize some previous $h$-stability results on this topic.

• 충청수학회지
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• 제29권1호
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• pp.1-11
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• 2016

This paper shows that the solutions to nonlinear perturbed functional differential system $$y^{\prime}=f(t,y)+{\int}^t_{t_0}g(s,y(s),Ty(s))ds+h(t,y(t))$$ have the asymptotic property by imposing conditions on the perturbed part ${\int}^t_{t_0}g(s,y(s),Ty(s))ds,h(t,y(t))$ and on the fundamental matrix of the unperturbed system y' = f(t, y).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권1호
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• pp.35-41
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• 1995

We consider the linear differential equations y〃'＋ P($\chi$)y'＋Q($\chi$)y=0 (1)(y"＋P($\chi$)y)'-Q($\chi$)y =0 (2) Where (2) in the adjoint of (1) and P($\chi$), Q($\chi$) are continuous functions satisfying P($\chi$)$\geq$0, Q($\chi$)$\leq$0, P($\chi$)-Q($\chi$)$\geq$0 on [a, ${\alpha}$). (3) In this, we show that a condition a oscillatory of(1).(omitted)

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권1호
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• pp.27-33
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• 1997

Let (M = B$\times$f F, g) be an ($n \geq3$ )-dimensional differential manifold with Riemannian metric g. We solve the following elliptic nonlinear partial differential equation (equation omitted). where $\Delta_{g}$ is the Laplacian in the $\Delta$g-metric and ($h(\chi)$) is the scalar curvature of g and ($H(\chi)$) is a function on M.

• 충청수학회지
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• 제7권1호
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• pp.123-139
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• 1994

In this paper we are concerned with optimal control problems whose costs are quadratic and whose states are governed by linear delay differential equations and general boundary conditions. The basic new idea of this paper is to introduce a new class of linear operators in such a way that the state equation subject to a starting function can be viewed as an inhomogeneous boundary value problem in the new linear operator equation. In this way we avoid the usual semigroup theory treatment to the problem and use only linear operator theory.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제3권1호
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• pp.47-52
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• 1996

We consider the third order linear homogeneous differential equation L$_3$(y) = y(equation omitted) ＋ P($\chi$)y' ＋ Q($\chi$)y = 0 (E) P($\chi$) $\geq$ 0, Q($\chi$) ＞ 0 and P($\chi$)/Q($\chi$) is nondecreasing on [${\alpha}$, $\infty$) for some real number ${\alpha}$. (1) In this paper we discuss the distribution of zeros of solutions and a condition of oscillatory for equation (E).(omitted)