On the Component Analysis and Transformation of An Explicit Fifth – Stage Fourth – Order Runge – Kutta Methods

Authors

  • Agbeboh Goddy Ujagbe Department of Mathematics, Ambrose Alli University, Ekpoma, Edo State, Nigeria
  • Esekhaigbe Aigbedion Christopher Department of Statistics, Auchi Polytechnic, Auchi, Edo State, Nigeria

DOI:

https://doi.org/10.18488/journal.24/2015.4.2/24.2.76.100

Abstract

This work is designed to transform the fifth stage – fourth order explicit Runge-Kutta method with the aim of projecting a new method of implementing it through tree diagram analysis. Efforts will be made to represent the equations derived from the y derivatives and x,y derivatives separately on Butcher’s rooted trees. This is because the rooted trees and derived equations for the y derivatives and x,y derivatives are the same for the explicit fourth-stage fourth-order methods, hence, we are motivated to analyze the fifth-stage fourth-order method. This idea is also derivable from general graphs and combinatorics.

Keywords:

Rooted tree diagram, Transformation, Vertex, Explicit, Y partial derivatives, X,Y partial derivatives, Linear and non- linear equations, Taylor series, Graphs

Abstract Video

Published

2016-01-02

How to Cite

Ujagbe, A. G. ., & Christopher, E. A. . (2016). On the Component Analysis and Transformation of An Explicit Fifth – Stage Fourth – Order Runge – Kutta Methods. International Journal of Mathematical Research, 4(2), 76–100. https://doi.org/10.18488/journal.24/2015.4.2/24.2.76.100

Issue

Vol. 4 No. 2 (2015)

Section

Articles