A Fourth Order Embedded Runge-Kutta RKACeM(4,4) Method Based on Arithmetic and Centroidal Means with Error Control

Murugesan, K.; Dhayabaran, D. Paul; Amirtharaj, E. C. Henry; Evans, David

doi:10.1080/00207160211925

Cited by 19 publications

(13 citation statements)

References 10 publications

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“…This embedded method has been developed using Runge-Kutta methods based on arithmetic mean (RKAM) and contraharmonic mean (RKCoM). Murugesan et al [9] introduced embedded centroidal mean, and Yaacob and Sanugi [10] adapted embedded harmonic mean.…”

Section: Introductionmentioning

confidence: 99%

A new fourth order embedded RKAHeM(4,4) method with error control on multilayer raster cellular neural network

Ponalagusamy

Senthilkumar

2007

SIViP

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We introduce a new technique for solving initial value problems (IVPs) with error control by formulating an embedded method involving RK methods based on arithmetic mean (AM) and Heronian mean (HeM). The function of the simulator is that it is capable of performing raster simulation for any kind as well as any size of input image. It is a powerful tool for researchers to examine the potential applications of CNN. By using the newly proposed embedded method, a versatile algorithm for simulating multilayer CNN arrays is implemented. This article proposes an efficient pseudo code for exploiting the latency properties of CNN along with well known RK-fourth order embedded numerical integration algorithms. Simulation results and comparison have also been presented to show the efficiency of the numerical integration algorithms. It is found that the RK-embedded Heronian mean outperforms well in comparison with the RK-embedded centroidal mean, harmonic mean and contra-harmonic mean. A more quantitative analysis has been carried out to clearly visualize the goodness and robustness of the proposed algorithm.

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Section: Introductionmentioning

confidence: 99%

A new fourth order embedded RKAHeM(4,4) method with error control on multilayer raster cellular neural network

Ponalagusamy

Senthilkumar

2007

SIViP

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“…R.Kutta approaches are useful to define numerical solutions for the complications, which are showed as differential equations relating Initial Value Problems that happen in the domains of industrial by Alexander & Coyle (1990;Dekker & Verwer, 1984;Evans, 1991a;Evans & Yaakub, 1996, 1998Hairer & Wanner, 1996;Murugesan, Dhayabaran, Amirtharaj, & Evans, 2002;Murugesan, Dhayabarin, Amirtharaj, & Evans, 2001;Murugesan, Dhayabarin, & Evans, 1999a, 2000Yaakub & Evans, 1999a. The R.Kutta method had been initiated at the twentieth century.…”

Section: Introductionmentioning

confidence: 99%

A numerical approach for solving problems in robotic arm movement

ALSultan

Ali

Hamid

2018

Production & Manufacturing Research

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Mechanical robotic arm control problems are examined in the numerical solutions for the second order system with the R. Kutta algorithms. The dynamics of a robotic arm be able to designated by a set of combined non-linear equations in the formula of coriolis, centrifugal effects and gravitational torques. This investigation attempted to minimize the error of an industrial robotic arm, which improves production systems. Results of comparisons illustrate the effectiveness of the numerical integrating algorithm based on the actual joint velocities and positions with each instant of time between the exact and numerical solutions. The obtained tables of data help to analyze the variation in the velocity and position joints at different time. The numerical results obtained by R.kutta-techniques perfectly match with the exact velocities. Depending on the relative error calculated at the obtained tables of results to reach the required motion of the mechanical robot arm.

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“…An example of which is the popular, albeit obsolete, method of Gill (1951), which selected a set of RK coefficients that required fewer space in the computer memory. However, a review of literature for the existence of fourth order versions, revealed a relatively low number existed [1,3,12,[16][17][18][19][20] of which, the classical fourth order RK method is the most used version.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Selected Versions of Fourth Order Runge-Kutta Algorithms as Simulation Tools for Harmonically Excited Duffing Oscillator

Salau

Adeleke

2018

ACRI

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This study aim is to investigate the properties of selected fourth order Runge-Kutta algorithms. Fiftyfive versions of fourth order Runge-Kutta (RK_1, RK_2, RK_3 …, RK_55) methods; inclusive of the classical fourth order RK version, were selected. Thereafter, these versions were used to simulate, with a constant and adaptive step-size algorithm, the dynamics of the harmonically excited Duffing Oscillator over a range of parameters and initial conditions. The simulation was carried out with a FORTRAN program developed and validated by comparing the program generated Poincaré section with literature standard. The number of successive steps taken between start and end of simulation periods was recorded for each simulation run. A total of 91809 simulations were run. The number of successive steps taken between start and end of simulation periods show that significant variations exists among different versions of the same Runge-Kutta order used for seeking solution of Duffing oscillator dynamics. Ranking results by the number of successive steps showed that RK_55 is not the fastest version available, despite its popularity, as other versions including RK_17, RK_2, RK_14, RK_20, and RK_8 outperformed it. Furthermore, the version performance was observed to be highly dependent on the excitation frequency, but not on initial conditions.

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A Fourth Order Embedded Runge-Kutta RKACeM(4,4) Method Based on Arithmetic and Centroidal Means with Error Control

Cited by 19 publications

References 10 publications

A new fourth order embedded RKAHeM(4,4) method with error control on multilayer raster cellular neural network

A new fourth order embedded RKAHeM(4,4) method with error control on multilayer raster cellular neural network

A numerical approach for solving problems in robotic arm movement

Investigation of Selected Versions of Fourth Order Runge-Kutta Algorithms as Simulation Tools for Harmonically Excited Duffing Oscillator

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