Comparative Analysis of Some New Runge-Kutta Type Techniques on the Solution of First Order Initial Value Problem in Ordinary Differential Equations

Olaniyan Adegoke Stephen^1*, Akanbi Moses Adebowale^1,2, Wusu Ashiribo Senapon¹, Kazeem Moshood Tolulope¹ and Akewushola Remilekun Jamiu¹

Abstract

The derivation of numerical methods to deal with differential equations framed from real life problems has been on the rise of which great deal of attention have been drawn towards Runge-kutta methods. In recent times, researchers have explored the derivation of Runge-Kutta methods by introducing higher order derivative (up to the second order) in the   terms of Runge-Kutta methods. We have also seen how other types of ‘mean’ are used as a substitute to the more usually applied arithmetic mean in the derivation Runge Kutta methods. However, in this paper some new Runge-Kutta type methods which border on the use of other types of ‘mean’ such as harmonic mean, geometric mean or heronian mean with higher derivatives up to the second derivative on a single explicit Runge-Kutta methods which were previously done on different explicit Runge-Kutta methods are constructed, analyzed, implemented and compared. The qualitative features of the methods including the local truncation error, consistency, convergence and stability of the new methods were comparatively analyzed, investigated and established. We demonstrated the validity of the comparisons with four numerical examples. The obtained results were compared with some numerical methods and the exact solutions of the proposed problems.

Keywords

initial value problems; explicit runge-kutta methods; heronian mean; geometric mean; harmonic mean

Cite This Article

Stephen, O. A., Adebowale, A. M., Senapon, W. A., Tolulope, K. M., Jamiu, A. R., (2024). Comparative Analysis of Some New Runge-Kutta Type Techniques on the Solution of First Order Initial Value Problem in Ordinary Differential Equations. International Journal of Scientific Advances (IJSCIA), Volume 5| Issue 3: May-Jun 2024, Pages 415-422, URL: https://www.ijscia.com/wp-content/uploads/2024/05/Volume5-Issue3-May-Jun-No.602-415-422.pdf

Volume 5 | Issue 3: May-Jun 2024