Title: Numerical solution of singular autonomous systems using the fourth-stage geometric mean Runge-Kutta method

Authors: Vijeyata Chauhan; Pankaj Kumar Srivastava

Addresses: Department of Mathematics, Jaypee Institute of Information Technology, Noida-201304, India ' Department of Mathematics, Jaypee Institute of Information Technology, Noida-201304, India

Abstract: The numerical treatment of singular problems is always seen to be intriguing, and its significance grows when it is raised in an autonomous system. This study proposes the development and implementation of a potent Runge-Kutta based fourth-stage explicit algorithm to numerically treat differential equations arising in the singular autonomous system. The basic properties of geometric mean have been brought into play to develop the algorithm. The convergence of the method has been established to prove the efficacy of the proposed technique. The consistency and stability of the method are also discussed. Two numerical illustrations are covered in the study, and the results are compared with some other existing conventional methods, which confirms the importance of the method. The proposed method is found more efficient not only in terms of accuracy but also for applicability in first-order differential equations.

Keywords: explicit Runge-Kutta method; singular autonomous system; geometric mean; differential equations; increment function.

DOI: 10.1504/IJDSDE.2025.148517

International Journal of Dynamical Systems and Differential Equations, 2025 Vol.14 No.3, pp.199 - 213

Received: 06 Dec 2024
Accepted: 17 Feb 2025
Published online: 10 Sep 2025 *

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