• Surendra Kumar Srivastava
• Shivani Tiwari

This present paper focused on the error analysis of first order ordinary differential equations through Runge-Kutta methods and Butcher’s 5th order method for solving initial value problem (IVP) through manually and MATLAB. In order to achieve higher accuracy in the solution of ordinary differential equations concerning the several functions, the step size needs to be very small. Numerical solution of ODE contains two types of error. One of them is Round off errors and second of them is truncation errors. Both errors generally occur when ODE (Initial value problem as well as Boundary value problem) are solved numerically. Round off error is originated to represent the significant figures in computers while truncation errors arise when approximations are used to estimate the some quantity

Initial value problem, Runge-Kutta method, Butcher’s 5th order Runge-Kutta method, MATLAB.

" A Comparative Study On Second Order, Third Order, Fourth Order& Butcher’s Fifth Order Runge-Kutta Methods With First Order Initial Value Problem(IVP) Through Manually And MATLAB", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 5, page no.335-343, May-2019, Available :http://www.jetir.org/papers/JETIR1905N51.pdf

" A Comparative Study On Second Order, Third Order, Fourth Order& Butcher’s Fifth Order Runge-Kutta Methods With First Order Initial Value Problem(IVP) Through Manually And MATLAB", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 5, page no. pp335-343, May-2019, Available at : http://www.jetir.org/papers/JETIR1905N51.pdf