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
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More From: Journal of the Nigerian Society of Physical Sciences
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