Open AccessAn Optimized 5-Point Block Formula for Direct Numerical Solution of First Order Stiff Initial Value Problems
Author(s) -
VO Atabo,
PO Olatunji
Publication year - 2020
Publication title -
nigerian journals of pure and applied sciences (benue online)
Language(s) - English
Resource type - Journals
ISSN - 2705-3997
DOI - 10.46912/napas.169
Subject(s) - collocation (remote sensing) , mathematics , convergence (economics) , interpolation (computer graphics) , ordinary differential equation , ode , initial value problem , block (permutation group theory) , power series , focus (optics) , constant (computer programming) , linear multistep method , series (stratigraphy) , mathematical analysis , differential equation , computer science , geometry , animation , differential algebraic equation , programming language , paleontology , physics , computer graphics (images) , machine learning , optics , economics , biology , economic growth
In this research article, we focus on the formulation of a 5-point block formula for solving first order ordinary differential equations (ODEs). The method is formulated via interpolation and collocation approach using power series expansion as the approximate solution. It has been established that the derived method is of order six. Basic properties such zero and absolute stabilities, convergence, order and error constant have also been investigated. The accuracy of the method was verified on some selected stiff IVPs, compared with some existing methods (DIBBDF, SDIBBDF, BBDF(4), BBDF(5) and odes15s) and test performance showed that the new method is viable.