Title: Numerical approximation of population growth in an autonomous system through a fourth-stage geometric mean-based explicit 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 future prediction of population numbers is an important factor in effectively managing the population models. A rise of pandemics like Covid-19 and its mutated versions have enhanced the need of standard numerical prediction method. The proposed study introduces a tetra geometric mean based explicit fourth order Runge-Kutta method to deal with population growth autonomous system which arises in population dynamics or economic industries or in chemical reactions or in biological growth models etc. In present study, two such numerical problems based on transmission of infectious disease have been solved. A one step explicit Runge-Kutta based numerical technique has been developed to solve such differential equation models. The convergence establishment of the developed method boosted the effectiveness of the proposed scheme. Through pandemics based numerical illustrations, the proposed method is examined and compared with other competing methods and that is found more amiable than other fourth order methods.

Keywords: Verhulst equation; logistic model of population explicit Runge-Kutta method; geometric mean; autonomous initial value problem.

DOI: 10.1504/IJCSM.2023.131456

International Journal of Computing Science and Mathematics, 2023 Vol.17 No.3, pp.241 - 253

Received: 01 Sep 2021
Received in revised form: 25 Sep 2022
Accepted: 08 Nov 2022
Published online: 13 Jun 2023 *

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