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A Comparative Study on Fourth Order and Butcher’s Fifth Order Runge-Kutta Methods with Third Order Initial Value Problem (IVP)
Applied and Computational Mathematics
Volume 6, Issue 6, December 2017, Pages: 243-253
Received: Sep. 26, 2017; Accepted: Oct. 8, 2017; Published: Nov. 8, 2017
Authors
Md. Babul Hossain, Department of Mathematics, Mawlana Bhashani Science and Technology University, Tangail-1902, Bangladesh
Md. Jahangir Hossain, Department of Basic Science, World University of Bangladesh, Dhaka, Bangladesh
Md. Musa Miah, Department of Mathematics, Mawlana Bhashani Science and Technology University, Tangail-1902, Bangladesh
Md. Shah Alam, Department of Mathematics, Mawlana Bhashani Science and Technology University, Tangail-1902, Bangladesh
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Abstract
In this paper, Butcher’s fifth order Runge-Kutta (RK5) and fourth order Runge-Kutta (RK4) methods have been employed to solve the Initial Value Problems (IVP) involving third order Ordinary Differential Equations (ODE). These two proposed methods are quite proficient and practically well suited for solving engineering problems based on such problems. To obtain the accuracy of the numerical outcome for this study, we have compared the approximate results with the exact results and found a good agreement between the exact and approximate solutions. In addition, to achieve more accuracy in the solution, the step size needs to be very small. Moreover, the error terms have been analyzed for these two methods and also compared by an appropriate example.
Keywords
Differential Equation, Initial Value Problem, Error, Butcher’s Method, Runge-Kutta Method
Md. Babul Hossain, Md. Jahangir Hossain, Md. Musa Miah, Md. Shah Alam, A Comparative Study on Fourth Order and Butcher’s Fifth Order Runge-Kutta Methods with Third Order Initial Value Problem (IVP), Applied and Computational Mathematics. Vol. 6, No. 6, 2017, pp. 243-253. doi: 10.11648/j.acm.20170606.12
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