ACCURATE BLOCK HYBRID METHODS FOR LARGE SCALE CHEMICAL KINETICSSIMULATIONS OF THE HIGH IRRADIANCE (HIRES) PROBLEM

Authors

  • Richard Olatokunbo Akinola
    University of Jos
  • Shangkum Yildum Goji
    University of Jos
  • Kyaharnan Victor Joshua
    University of Jos
  • Amin Miracle Daze
    University of Jos

Keywords:

Hires Problem, Block Hybrid, Absolute Stability, Interpolation, Collocation, Exact Solution

Abstract

This article presents two A(a), zero–stable, consistent and convergent methods for the numerical approximation of the High Irraddiance problem. The first method is a first derivative method while the second method is a second derivative block hybrid method for the numerical solution of initial problems most especially the High Irraddiance (HIRES) problem with origins from chemical kinetics. The first method is of order five with a small region of absolute stability, while the new second derivative method is of order nine with a large region of absolute stability as well as smaller error constants. The methods stems from the interpolation and collocation approach with un-equidistant give points. Sequel to using the methods in solving the HIRES problem which has no exact solution, we compared the performance of our second method with a method in a recent literature and the method outperformed it. This gave us the motivation in using the method to solve the problem under consideration

Author Biographies

Richard Olatokunbo Akinola

Enjoys programming in python, R, Octave, maxima.

Department of Mathematics

Faculty of Natural Sciences, University of Jos

Associate Professor

Shangkum Yildum Goji

A Chemist

Kyaharnan Victor Joshua

A Mathematician

Amin Miracle Daze

Department of Mathematics

Dimensions

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Convergence plot of Example 1 against t using the new second derivative block method

Published

22-10-2025

How to Cite

Akinola, R. O., Goji, S. Y., Joshua, K. V., & Daze, A. M. (2025). ACCURATE BLOCK HYBRID METHODS FOR LARGE SCALE CHEMICAL KINETICSSIMULATIONS OF THE HIGH IRRADIANCE (HIRES) PROBLEM. FUDMA JOURNAL OF SCIENCES, 9(11), 83-97. https://doi.org/10.33003/fjs-2025-0911-4073

Issue

Vol. 9 No. 11 (2025): FUDMA Journal of Sciences - Vol. 9 No. 11

Section

Research Articles
Copyright & Licensing

Copyright (c) 2025 Richard Olatokunbo Akinola, Shangkum Yildum Goji, Kyaharnan Victor Joshua, Amin Miracle Daze

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Akinola, R. O., Goji, S. Y., Joshua, K. V., & Daze, A. M. (2025). ACCURATE BLOCK HYBRID METHODS FOR LARGE SCALE CHEMICAL KINETICSSIMULATIONS OF THE HIGH IRRADIANCE (HIRES) PROBLEM. FUDMA JOURNAL OF SCIENCES, 9(11), 83-97. https://doi.org/10.33003/fjs-2025-0911-4073