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

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2019 by IJMTT Journal
Volume-65 Issue-10
Year of Publication : 2019
Authors : Mohammed Nizam Uddin, Mahmuda Akter, A.N.M Rezaul karim
  10.14445/22315373/IJMTT-V65I10P514

MLA

MLA Style: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 65.10 (2019):98-108.

APA Style: Mohammed Nizam Uddin, Mahmuda Akter, A.N.M Rezaul karim(2019).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,98-108

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.

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