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

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  • Agbeboh Goddy Ujagbe
  • Esekhaigbe Aigbedion Christopher

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.

Suggested Citation

  • Agbeboh Goddy Ujagbe & Esekhaigbe Aigbedion Christopher, 2015. "On the Component Analysis and Transformation of An Explicit Fifth – Stage Fourth – Order Runge – Kutta Methods," International Journal of Mathematical Research, Conscientia Beam, vol. 4(2), pages 76-100.
    • Handle: RePEc:pkp:ijomre:v:4:y:2015:i:2:p:76-100:id:2180
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