A comparative study of 4th-order and 6th-stage 5th-order Runge-Kutta methods for solving autonomous differential equations

Authors

  • Abubakar Salihu Department of Mathematics, Aliko Dangote University of Science and Technology, Wudil, Nigeria
  • Auwal Lawan Department of Mathematics, Aliko Dangote University of Science and Technology, Wudil, Nigeria https://orcid.org/0009-0000-8244-7786

DOI:

https://doi.org/10.64497/jssci.52

Keywords:

autonomous differential equation , initial value problem , Runge-Kutta method, absolute error

Abstract

In this study, we utilized the Sixth-Stage Fifth-Order Runge-Kutta method and the Fourth-Order Runge-Kutta (RK4) method to address First-Order Autonomous Differential Equations with Initial Value Problems (IVPs). Both methods demonstrate considerable efficacy and are well-suited for resolving challenges encountered in engineering and scientific contexts. To evaluate the accuracy of the numerical solutions obtained, we compared the approximate results with exact solutions, revealing a strong correlation between the two. Additionally, we analyzed the error terms associated with both methods and provided a comparative evaluation using a relevant example.

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Author Biography

Auwal Lawan, Department of Mathematics, Aliko Dangote University of Science and Technology, Wudil, Nigeria

Auwal Lawan is a graduate of mathematics from Aliko Dangote University of Science and Technology, Wudil Kano, Nigeria, Auwal graduated as the best students in his department, and was selected as the first and only African student for the Maths-Disc master degree program as a scholarship holder starting at University of Verona, Italy.

He is also a data scientist, machine learning, and AI practitioner.

References

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Published

2025-08-11

How to Cite

Salihu, A., & Lawan, A. (2025). A comparative study of 4th-order and 6th-stage 5th-order Runge-Kutta methods for solving autonomous differential equations. Journal of Statistical Sciences and Computational Intelligence, 1(2), 138–148. https://doi.org/10.64497/jssci.52

Issue

Vol. 1 No. 2 (2025): Volume 1, Issue 2

Section

Articles

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Copyright (c) 2025 Auwal Lawan, Abubakar Salihu

Creative Commons License

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

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