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System of second order robot arm problem by an efficient numerical integration algorithmKeywords: RK-Sixth-Order algorithm , Ordinary differential equations , System of second order , Robot arm problem Abstract: Purpose: The aim of this article is focused on providing numerical solutions for system of second order robot arm problem using the Runge-Kutta Sixth order algorithm.Design/methodology/approach: The parameters governing the arm model of a robot control problem have also been discussed through RK-sixth-order algorithm. The precised solution of the system of equations representing the arm model of a robot has been compared with the corresponding approximate solutions at different time intervals.Findings: Results and comparison show the efficiency of the numerical integration algorithm based on the absolute error between the exact and approximate solutions. The stability polynomial for the test equation ˙γ=λγ (λ is a complex Number) using RK-butcher algorithm obtained by Murugesan et. al. [1] and Park et. al. [2,3] is not correct and the stability regions for RK-Butcher methods have been absurdly presented. They have made a blunder in determining the range for real parts of λh (h is a step size) involved in the test equation for RK-Butcher algorithms. Further, they have abruptly drawn the stability region for STWS method assuming that it is based on the Taylor’s series technique.Research limitations/implications: It is noticed that STWS algorithm is not based on the Taylor’s series method and it is an A-stable method. In the present paper, a corrective measure has been taken to obtain the stability polynomial for the case of RK-Butcher algorithm, the ranges for the real part of λh and to present graphically the stability regions of the RK-Butcher methods.Originality/value: Based on the numerical results and graphs, a thorough comparison is carried out between the numerical algorithms.
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