Open AccessNumerical Solutions of Nonlinear Ordinary Differential Equations by Using Adaptive Runge-Kutta Method
Author(s) -
Abhinandan Chowdhury,
Sammie Clayton,
Mulatu Lemma
Publication year - 2019
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v17i0.8408
Subject(s) - runge–kutta methods , mathematics , nonlinear system , truncation error , ordinary differential equation , interval (graph theory) , initial value problem , limit (mathematics) , numerical integration , adaptive stepsize , truncation (statistics) , differential equation , numerical analysis , mathematical analysis , statistics , physics , quantum mechanics , combinatorics
We present a study on numerical solutions of nonlinear ordinary differential equations by applying Runge-Kutta-Fehlberg (RKF) method, a well-known adaptive Runge-kutta method. The adaptive Runge-kutta methods use embedded integration formulas which appear in pairs. Typically adaptive methods monitor the truncation error at each integration step and automatically adjust the step size to keep the error within prescribed limit. Numerical solutions to different nonlinear initial value problems (IVPs) attained by RKF method are compared with corresponding classical Runge-Kutta (RK4) approximations in order to investigate the computational superiority of the former. The resulting gain in efficiency is compatible with the theoretical prediction. Moreover, with the aid of a suitable time-stepping scheme, we show that the RKF method invariably requires less number of steps to arrive at the right endpoint of the finite interval where the IVP is being considered.