Solution of Differential Equations of the First Order via Different Order of Runge-Kutta method with it’s Application

Mohammed Nizam Uddin; Mahmuda Akter; A.N.M Rezaul karim

doi:https://doi.org/10.14445/22315373/IJMTT-V65I10P514

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 10 | Year 2019 | Article Id. IJMTT-V65I10P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I10P514

Solution of Differential Equations of the First Order via Different Order of Runge-Kutta method with it’s Application

Mohammed Nizam Uddin, Mahmuda Akter, A.N.M Rezaul karim

Citation :

Mohammed Nizam Uddin, Mahmuda Akter, A.N.M Rezaul karim, "Solution of Differential Equations of the First Order via Different Order of Runge-Kutta method with it’s Application," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 10, pp. 98-108, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I10P514

Abstract

This analysis is related to Runge-Kutta (R-K) approach of upper order and an application to resolve the problem with initial value of ordinary differential equations (ODE) with 1st order. The second order derivation, fourth order and sixth order Runge-Kutta process were first performed. MATLAB code was subsequently applied to solve the problem numerically for different order R-K method and calculating error with the analytical value. Then we have given the graphical representation different order of R-K method as well as an analytical solution for various problems. Comparing approximate values from the different order of R-K method with the analytical values in tabular form and graphical representation, we can observe that the R-K method of 6th order gives better precision.

Keywords

Runge-Kutta (R-K) method, ordinary differential equations, initial value problem

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