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

Agbeboh Goddy Ujagbe, Esekhaigbe Aigbedion Christopher

Abstract


This work is designed to transform the fourth 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 idea is derivable from general graphs and combinatorics.

Key words: Rooted tree diagram, Transformation, Vertex, explicit, y partial derivatives, x,y partial derivatives, Runge-Kutta Methods, Linear and non- linear equations, Taylor series, Graphs.

Keywords: key words, Runge - Kutta, Combinatorics, Derivatives, Transformation, Analysis


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ISSN (Paper)2224-3186 ISSN (Online)2225-0921

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