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Home  >  Volume 33

On the Rooted Tree and Component Analysis of an Explicit Fourth-Stage Fourth-Order Runge-Kutta Method by Agbeboh Goddy Ujagbe,Esekhaigbe Aigbedion Christopher and Akhanolu Aziegbe Gilbert (pages 61-70)
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The object of this work is to concentrate on the f(x,y) functional derivatives after using Taylor Series expansion to expand the fourth-stage fourth-order explicit Runge-Kutta method. Efforts will be made to vary the parameters with the aim of getting a fourth order formula that can improve results when implemented on initial-value problems. Efforts will also be made to represent the derived equations and their individual f(x,y) functional derivatives on Butcher’s rooted trees. This idea is derivable from general graphs and combinatorics.

                Keywords: Rooted tree diagram, Components, explicit, f(x,y) functional derivatives, Runge-Kutta Methods, Linear and non- linear equations, Taylor series, Graphs, Parameters, Initial-value Problems, Combinatorics