• 대한수학회보
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• 제35권1호
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• pp.157-172
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• 1998

A numerical method is proposed for dynamical systems. We utilize the fact that special matrix exponentials can be exactly evaluated by the intrinsic library functions. Numerical examples are given, which show that the relative error s of the proposed method converge to a small constant and that the method faithfully approximates the dynamics of the nonlinear differential equations.

• 대한수학회보
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• 제29권1호
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• pp.31-40
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• 1992

We introduce the generalized Runge-Kutta methods with the exponentially dominant order .omega. in [3], and the convergence theorems of the generalized explicit Euler method are derived in [4]. In this paper we will study the convergence of the generalized implicit Euler method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권4호
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• pp.238-266
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• 2013

The Interaction Picture (IP) method is a valuable alternative to Split-step methods for solving certain types of partial differential equations such as the nonlinear Schr$\ddot{o}$dinger equation or the Gross-Pitaevskii equation. Although very similar to the Symmetric Split-step (SS) method in its inner computational structure, the IP method results from a change of unknown and therefore do not involve approximation such as the one resulting from the use of a splitting formula. In its standard form the IP method such as the SS method is used in conjunction with the classical 4th order Runge-Kutta (RK) scheme. However it appears to be relevant to look for RK scheme of higher order so as to improve the accuracy of the IP method. In this paper we investigate 5th order Embedded Runge-Kutta schemes suited to be used in conjunction with the IP method and designed to deliver a local error estimation for adaptive step size control.

• The Journal of the Acoustical Society of Korea
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• 제25권1E호
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• pp.32-35
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• 2006

The screech tone of underexpanded jet is numerically calculated without any specific modeling for the screech tone itself. Fourth-order optimized compact scheme and fourth-order Runge-Kutta method are used to solve the 2D axisymmetric Euler equation. Adaptive nonlinear artificial dissipation model and generalized characteristic boundary condition are also used. The screech tone, generated by a closed loop between instability waves and quasi-periodic shock cells at the near field, is reasonably analyzed with present numerical methods for the underexpanded jet having Mach number 1.13. First of all, the centerline mean pressure distribution is calculated and compared with experimental and other numerical results. The instantaneous density contour plot shows Mach waves due to mixing layer convecting supersonically, which propagate downstream. The pressure signal and its Fourier transform at upstream and downstream shows the directivity pattern of screech tone very clearly. Most of all, we can simulate the axisymmetric mode change of screech tone very precisely with present method. It can be concluded that the basic phenomenon of screech tone including the frequency can be calculated by using high-order and high-resolution schemes without any specific numerical modeling for screech tone feedback loop.

• 한국지능시스템학회논문지
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• 제13권3호
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• pp.259-259
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• 2003

유전자 알고리즘은 생물의 유전적 진화과정을 이용한 새로운 문제 해결의 방안으로 결정론적 방법으로 해결하지 못한 난제에 적합한 알고리즘이다. 제어기 설계 기법은 주파수에 의존하는 명세에 의한 설계는 있어 왔으나 Manabe 표준형을 기본으로 사용하는 시간에 의존하는 명세를 만족시키는 제어기 설계 기법은 미미한 단계에 있다. 본 논문에서는 일반화된 Manabe 표준형을 이용하여 플랜트의 성능을 충족시키는 제어기의 설계에 관해 연구한다. 두 변수 구조를 갖는 제어시스템에서 제어기의 계수 설계시 역행렬 방법이나 기존의 의역 행렬 방법으로 해결할 수 없는 경우가 있다. 이 경우에 원하는 폐루프 다항식이 설계된 다항식과 같거나 근사적으로 같도록 새로운 의역 행렬 방법과 경사알고리즘을 이용하여 제어기를 설계하는 두 가지 방법을 제안한다. 다음으로 제안된 제어기 설계 방법들을 자바로 구현한다