V2I10P73

A Uniform Order Four-Step Hybrid Block Method for Numerical Solution of Susceptible-Infected-Recovered (SIR) and Growth Model

Shuaibu Lawan Nasidi^1*, Zayyanu Balarabe Bayawa¹, Saudat Sanni¹

Abstract

In this research work, we derived a uniform order four step hybrid block method for the numerical solution of Susceptible-Infected-Recovered (SIR) and Growth model problems of ordinary differential equations (ODEs). A continuous linear multistep method (CLMM) with variable coefficients was developed using interpolation and collocation techniques via power series approximate solution as the basis function. This CLMM was evaluated at some selected grids points which give a class of discrete linear multistep methods (DLMMs) and was implemented as a block method. One case was considered for step numbers k=4. The basic properties of the block method were investigated and found out to be of order nine, consistent, zero stable and hence convergent. MATLAB 2015 codes were written to test the numerical performance of the block method on some real-life problems of ordinary differential equation and the results showed that the four-step hybrid block method compared favorably with the existing methods in terms of accuracy and efficiency, was found to be very effective.

Keywords:

Hybrid block method; continuous linear multistep method; numerical solution; ordinary differential equations; SIR model