ROOTED TREE ANALYSIS OF AN EXPLICIT FOURTH-STAGE FOURTH ORDER RUNGE- KUTTA METHOD
DOI:
https://doi.org/10.53555/nnms.v9i8.1227Keywords:
Rooted tree diagram, Comparison, Variation, explicit, f(y) functional derivatives, (x,y) functional derivatives Runge-Kutta MethodAbstract
This research paper is aimed at using Butcher’s rooted trees to separate the f(y) functional derivatives from the f(x,y) functional derivatives after applying Taylor series expansion on the general fourth stage fourth order Runge Kutta method. This approach revealed that the f(y) functional derivatives generated a set of linear/ nonlinear equations that gave birth to a fourth stage fourth order Runge Kutta formula. This idea is derivable from general graphs and combinatorics.
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