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International Journal of Mathematical Research

April 2015, Volume 4, 2, pp 76-100

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

Agbeboh Goddy Ujagbe

,

Esekhaigbe Aigbedion Christopher

Agbeboh Goddy Ujagbe 1
Esekhaigbe Aigbedion Christopher 2

  1. Department of Mathematics, Ambrose Alli University, Ekpoma, Edo State, Nigeria. 1

  2. Department of Statistics, Auchi Polytechnic, Auchi, Edo State, Nigeria. 2

Pages: 76-100

DOI: 10.18488/journal.24/2015.4.2/24.2.76.100

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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.
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Reference:

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