Abstract
In this paper, we consider fourth order Runge-Kutta method for solving ordinary differential equations in initial value problems. The proposed methods are quite efficient and are practically well suited for solving these problems. Several examples are presented to demonstrate the accuracy and easy implementation of the proposed methods. The results of numerical experiments are compared with the analytical solution and thereby gain some insight into the accuracy of proposed methods. Finally we investigate and compute the error of proposed methods. This counterintuitive result is analyzed in this paper.
Highlights
Many problems of mathematical physics can be started in the form of differential equations
Numerical methods are commonly used for solving mathematical problems that are formulated in science and engineering where it is difficult or even impossible to obtain exact solutions
Even there exist a large number of ordinary differential equations whose solutions cannot be obtained in closed form by using well known analytical methods, where we have to use the numerical methods to get the approximate solution of a differential equation under the prescribed initial condition or conditions
Summary
Many problems of mathematical physics can be started in the form of differential equations. Even there exist a large number of ordinary differential equations whose solutions cannot be obtained in closed form by using well known analytical methods, where we have to use the numerical methods to get the approximate solution of a differential equation under the prescribed initial condition or conditions. From the literature review we may realize that several works in numerical solutions using fourth order Runge-Kutta method and many authors have attempted to solve initial value problems (IVP) to obtain high accuracy rapidly by using a numerous methods, such as Euler methods, and some other methods. In this paper we apply fourth order Runge-Kutta method for solving ordinary differential equation in initial value problems. A more robust and intricate numerical technique is the Runge-Kutta method This method is the most widely used one since it gives reliable starting values and is suitable when the computation of higher derivatives is complicated. The results of each numerical example indicate the convergence and error analysis is discussed to illustrate the efficiency of the method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
