PARAMETRIC VARIATION OF AN EXPLICIT FOURTH-STAGE FOURTH ORDER RUNGE-KUTTA METHOD WITH ABSOLUTE STABILITY

Authors

  • Esekhaigbe Aigbedion Christopher Department of Mathematics, Aduvie Pre-University College, Jahi, Abuja, Nigeria.
  • Akeem Disu Disu Akeem, Dept. of Mathematics, National Open University, Abuja
  • Luke Ukpebor Ukpebor Luke, Dept. of Mathematics, Ambrose Alli University, Ekpoma

DOI:

https://doi.org/10.53555/nnms.v9i8.839

Keywords:

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 differentials

Abstract

The purpose of this paper is to separate the  functional derivatives by discarding all functional derivatives of  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  functional derivatives and their various elementary differentials on Butcher’s rooted trees. This idea is derivable from general graphs and combinatorics.

References

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Published

2022-08-22

How to Cite

Christopher, E. A. ., Akeem Disu, & Ukpebor, L. . (2022). PARAMETRIC VARIATION OF AN EXPLICIT FOURTH-STAGE FOURTH ORDER RUNGE-KUTTA METHOD WITH ABSOLUTE STABILITY. Journal of Advance Research in Mathematics and Statistics (ISSN 2208-2409), 9(8), 1-7. https://doi.org/10.53555/nnms.v9i8.839

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