PARAMETRIC VARIATION OF AN EXPLICIT FOURTH-STAGE FOURTH-ORDER RUNGE-KUTTA METHOD WITH ABSOLUTE STABILITY
DOI:
https://doi.org/10.61841/1ka29j30Keywords:
Rooted tree diagram, Comparison, Variation, explicit, y partial derivatives, Runge-Kutta Methods, Linear and non- linear equations, Taylor series, Graphs, Parameters, Initial-value Problems, Combinatorics, f(y) functional derivatives, elementary differentialsAbstract
The purpose of this paper is to separate the f(y) functional derivatives by discarding all functional derivatives of f(x,y) after using Taylor Series expansion to expand the fourth-stage fourth-order explicit Runge-Kutta method so as to derive a reduced number of equations for easy computation. Efforts will be made to vary the parameters with the aim of getting a new explicit fourth-order formula that can improve results when implemented on initial-value problems. Efforts will also be made to carry out stability, convergence and consistency analysis and represent the derived equations, their individual f(y) functional derivatives and their various elementary differentials on Butcher’s rooted trees. This idea is derivable from general graphs and combinatorics.
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