Please use this identifier to cite or link to this item: http://ir.lib.seu.ac.lk/handle/123456789/3488
Title: A comparative study on solving first order ordinary differential equations using numerical methods
Authors: Fasmie, N. M.
Fajila, M. N. F.
Keywords: Ordinary differential equations
Numerical methods
Euler method
Runge Kutta method.
Issue Date: 15-Nov-2018
Publisher: Faculty of Applied Science, South Eastern University of Sri Lanka
Series/Report no.: Abstracts of the 7th Annual Science Research Sessions (ASRS) – 2018;36
Abstract: Ordinary differential equations (ODEs) are widely applicable in numerous fields such as in population dynamics and bioscience. Practically, it is too difficult to solve complex differential equations to obtain an exact solution and hence, approximation methods are used for the solutions. In this paper, we used numerical methods to solve first order ODEs. There are several numerical methods among which Euler Method and the fourth order Runge Kutta (RK4) Method were compared in this proposed study. The first order ODE, 𝑑𝑦 𝑑𝑡 = 𝑡 2 + 𝑦 , 𝑦(0) = 1 was used for the implementation of proposed approach. According to the findings, the maximum error obtained for each method namely Euler and RK4 are proportional to ℎ and ℎ 4 to each method respectively where, ℎ denote the step size. The results obtained in this study show that RK4 performs well for ODEs with near approximate solutions with less error. Further, it is obvious that step size vastly influences the performance as when step size decreased the approximate solution approached to near original solution. We implemented the proposed approach with a suitable example of first order ODE as given in the above equation to compare and illustrated the fact that numerical methods provide acceptable near approximate solution to solve ODEs.
URI: http://ir.lib.seu.ac.lk/handle/123456789/3488
ISBN: 9789556271362
Appears in Collections:ASRS - FAS 2018

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