Title: Insight into 2-step continuous block method for solving mixture model and SIR model

Authors: M.K. Duromola; A.L. Momoh; M.A. Rufai; I.L. Animasaun

Addresses: Department of Mathematical Sciences, Federal University of Technology, Akure, PMB 704, Nigeria ' Department of Mathematical Sciences, Federal University of Technology, Akure, PMB 704, Nigeria ' Department of Mathematical Sciences, Federal University of Technology, Akure, PMB 704, Nigeria ' Department of Mathematical Sciences, Federal University of Technology, Akure, PMB 704, Nigeria

Abstract: Understanding of the solutions of first-order ordinary differential equations (ODEs), mixture model and SIR model in order to develop deep insight and exploration are major problems before the experts, biologists, scientists, and mathematicians. In all these problems, the governing equations are either single first-order or coupled ODEs kind of initial value problem (IVP). In this paper, a polynomial function q(x) that passes through the points (x_n, y_n), (x_n+1, y_n+1), . . . , (x_n+2, y_n+2) was adopted as the basis function that leads to third derivatives continuous 2-step block method suitable to solve first order initial value problems of ODEs. Upon using the newly proposed scheme to solve linear ODEs (i.e., mixture theory) and nonlinear ODE (i.e., SIR model), it is worth concluding that the algorithm is not only efficient but minimises error.

Keywords: 2-step method; first order ODEs; continuous schemes; multi-step collocation; third derivative formula; block method; mixture model; SIR Model.

DOI: 10.1504/IJCSM.2021.120684

International Journal of Computing Science and Mathematics, 2021 Vol.14 No.4, pp.347 - 356

Received: 02 Apr 2020
Accepted: 11 Jun 2020
Published online: 03 Feb 2022 *

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