Open AccessAn Efficient Seven-Step Block Method for Numerical Solution of SIR and Growth Model
Author(s) -
O. E. Abolarin,
Gbenga B Ogunware,
Lukman Shina Akinola
Publication year - 2020
Publication title -
fuoye journal of engineering and technology
Language(s) - English
Resource type - Journals
eISSN - 2579-0625
pISSN - 2579-0617
DOI - 10.46792/fuoyejet.v5i1.490
Subject(s) - linear multistep method , block (permutation group theory) , interpolation (computer graphics) , collocation (remote sensing) , mathematics , constant (computer programming) , series (stratigraphy) , interval (graph theory) , power series , algorithm , computer science , mathematical optimization , mathematical analysis , differential equation , ordinary differential equation , geometry , animation , differential algebraic equation , paleontology , computer graphics (images) , combinatorics , machine learning , biology , programming language
In this article, a new implicit continuous block method is developed using the interpolation and collocation techniques via Power series as the basis function. A constant step length within a seven-step interval of integration was adopted. The selected grid points were evaluated to get a continuous linear multistep method. The evaluation of the continuous method at the non-interpolation points produces the discrete schemes which form the block. The basic properties of the block method were investigated and found to be consistent, zero stable and hence convergent. The new method was tested on real life problems namely: SIR and Growth model. The results were found to compare favourably with the existing methods in terms of accuracy and efficiency. Keywords: Block method, Growth Model, implicit, power series and SIR model.
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