• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.191-204
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• 2017

A new fifth-order weighted Runge-Kutta algorithm based on heronian mean for solving initial value problem in ordinary differential equations is considered in this paper. Comparisons in terms of numerical accuracy and size of the stability region between new proposed Runge-Kutta(5,5) algorithm, Runge-Kutta (5,5) based on Harmonic Mean, Runge-Kutta(5,5) based on Contra Harmonic Mean and Runge-Kutta(5,5) based on Geometric Mean are carried out as well. The problems, methods and comparison criteria are specified very carefully. Numerical experiments show that the new algorithm performs better than other three methods in solving variety of initial value problems. The error analysis is discussed and stability polynomials and regions have also been presented.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.657-670
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• 2015

In this paper, we provide numerical analysis of so-called Legendre Gauss-Radau and Legendre-Gauss collocation methods for ordinary differential equations. After recasting these collocation methods as Runge-Kutta methods, we prove that the Legendre-Gauss collocation method is equivalent to the well-known Gauss method, while the Legendre-Gauss-Radau collocation method does not belong to the classes of Radau IA or Radau IIA methods in the Runge-Kutta literature. Making use of the well-established theory of Runge-Kutta methods, we study stability and accuracy of the Legendre-Gauss-Radau collocation method. Numerical experiments are conducted to confirm our theoretical results on the accuracy and numerical stability of the Legendre-Gauss-Radau collocation method, and compare Legendre-Gauss collocation method with the Gauss method.

• International journal of advanced smart convergence
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• 제2권1호
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• pp.18-20
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• 2013

The significance, is to introduce a novel way to employ the improved Runge-Kutta fifth order five stage method, here after called as Modified IRK(5,5) method, for system of second order robot arm problem and variations in angles at the joints in which parameters governing with two degrees of freedom which requires lesser number of function evaluations per time step as compared to the existing ones, in order to save time and spaceAn ultimate aim of this present paper is to solve application problem such as robot arm and initial value problems by applying Runge-Kutta fifth order five stage numerical techniques. The calculated output for robot arm coincides with exact solution which is found to be better, suitable and feasible for solving real time problems.

• 한국측량학회지
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• 제28권6호
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• pp.573-578
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• 2010

위성항법시스템에서 정확한 위성궤도결정 기술은 측위 정확도 향상의 필수적인 조건이다. 이 연구에서는 GLONASS의 방송궤도력과 4차 Runge-Kutta 수치적분법을 이용하여 위성좌표를 결정하였으며, 적분간격과 적분시간에 따른 위성궤도의 정확도를 비교하였다. 적분간격에 따른 위성궤도 정확도분석결과, 적분간격이 l초일 때와 300초일 때의 3차원 RMS 오자의 차이가 3cm에 불과한 반면 처리시간은 100배 이상 향상되었다. 적분시간에 따른 위성좌표의 3차원 RMS 오차는 적분시간이 30분, 150분, 300분일 때 각각 8.3m, 187.3m, 661.5m로 나타났으며, 이를 통해 적분시간을 짧게 할수록 정확도가 향상되는 것을 확인하였다. 따라서 이 연구에서는 GLONASS 측위를 위한 위성좌표 결정의 정확도 향상을 위해 적분시간을 최소화할 수 있는 Forward와 Backward 적분을 적용하는 방안을 제안하였으며, 이와 같은 방법을 사용할 경우 5m이하의 위성좌표 산출 정확도를 확보할 수 있다.

• Mass Spectrometry Letters
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• 제6권3호
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• pp.59-64
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• 2015

Quadrupole ion trap mass analyzer with a simplified geometry, namely, the cylindrical ion trap (CIT), has been shown to be well-suited using in miniature mass spectrometry and even in mass spectrometer arrays. Computation of stability regions is of particular importance in designing and assembling an ion trap. However, solving CIT equations are rather more difficult and complex than QIT equations, so, analytical and matrix methods have been widely used to calculate the stability regions. In this article we present the results of numerical simulations of the physical properties and the fractional mass resolutions m/Δm of the confined ions in the first stability region was analyzed by the fifth order Runge-Kutta method (RKM5) at the optimum radius size for both ion traps. Because of similarity the both results, having determining the optimum radius, we can make much easier to design CIT. Also, the simulated results has been performed a high precision in the resolution of trapped ions at the optimum radius size.

• Smart Structures and Systems
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• 제15권5호
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• pp.1311-1327
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• 2015

In this paper, we have applied a new class of approximate analytical methods called Variational Approach (VA) for high nonlinear vibration equations. Three examples have been introduced and discussed. The effects of important parameters on the response of the problems have been considered. Runge-Kutta's algorithm has been used to prepare numerical solutions. The results of variational approach are compared with energy balance method and numerical and exact solutions. It has been established that the method is an easy mathematical tool for solving conservative nonlinear problems. The method doesn't need small perturbation and with only one iteration achieve us to a high accurate solution.

• 한국기계가공학회지
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• 제5권3호
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• pp.36-42
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• 2006

The analytical realization of uncoupled system was introduced in this study using times series and its spectrum analysis. The ARMAX spectra of time series methods were compared with the conventional FFT spectrum. Also, the response of second order system uncoupled was solved using the Runge-Kutta Gill method. In this numerical analysis, the displacement, velocity and acceleration were calculated. The displacement response among them was used for the power spectrum analysis. The ARMAX algorithm in time series was proved to be appropriate for the mode estimation and spectrum analysis. Using the separate response of first and second mode, each modes were calculated separately and the response of mixed modes was also analyzed for the mode estimation using several time series methods.