Open AccessSEMI-IMPLICIT RATIONAL RUNGE-KUTTA METHOD OF SOLVING SECOND ORDER DIFFERENTIAL EQUATION
Author(s) -
Eric Augustine Oje,
Aggrey Eric Majuk
Publication year - 2020
Publication title -
international journal of engineering applied science and technology
Language(s) - English
Resource type - Journals
ISSN - 2455-2143
DOI - 10.33564/ijeast.2020.v04i09.011
Subject(s) - runge–kutta methods , differential equation , mathematics , order (exchange) , mathematical analysis , economics , finance
There is much work done on implicit and explicit rational Runge-Kutta schemes for second order ordinary differential equations. This motivated the need for semi-implicit scheme since no work has been done on it for second order ordinary differential equations. The research was carried out using Taylor‟s series and Binomial expansion after some related works were reviewed in the literature. The research was completed in which a one-stage semi-implicit rational RungeKutta scheme was derived, the convergence and consistency of the scheme was tested and the scheme was convergent and consistent. The adopted scheme was discovered to perform well in terms of approximating the exact solution of a special case of second order ordinary differential equations. Keywords— ordinary differential equations, Runge-Kutta, semi-implicit scheme