Abstract
Runge-Kutta methods are efficient methods of computations in differential equations, the classical Runge-Kutta method of order 4 happens to be the most popular of these methods, and most times it is attached to the mind when Runge-Kutta methods are mentioned. However, there are numerous forms of them existing in lower and higher orders of the classical method. This work investigates the linear stabilities and abilities of some selected explicit members of these Runge-Kutta methods in integrating the singular Lane-Emden differential equations. The results obtained established the ability of the classical Runge-Kutta method and why is mostly used in computations.
Highlights
Runge-Kutta methods are efficient methods of computations in differential equations, the classical Runge-Kutta method of order 4 happens to be the most popular of these methods, and most times it is attached to the mind when Runge-Kutta methods are mentioned
The most popular of the methods of Runge-Kutta is the classical Runge-Kutta method of order 4, ’classical’ as related to the method obtained in the pre-computer era
Sci. 2 (2020) 134–140 problems have proved to be either difficult to solve or cannot in the solution of singular Lane-Emden problems of ordinary be solved analytically due to the singularity as the approximate differential equations
Summary
This is a behaviourial property related to h > 0. The linear stability will be analyzed using the Dalquist’s test y (t) = γy(t), (γ) < 0. Applying methods (9)-(16) on (17), we have obtained a recurrence equation yi = M(z)yi−1. Where M(z = hγ) for each of the method is given in Table 1 below The contour for regions of absolute stability as obtained from their characteristics equations are given in Figure 1 - 8
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 callMore From: Journal of the Nigerian Society of Physical Sciences
Disclaimer: 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.
