Open AccessDirect Solution of Second Order Ordinary Differential Equations Using a Class of Hybrid Block Methods
Author(s) -
E. A. Areo,
Nosimot O Adeyanju,
John Stephen Kayode
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.v5i2.537
Subject(s) - ordinary differential equation , mathematics , linear multistep method , initial value problem , convergence (economics) , consistency (knowledge bases) , block (permutation group theory) , grid , function (biology) , class (philosophy) , differential (mechanical device) , series (stratigraphy) , stability (learning theory) , basis (linear algebra) , differential equation , mathematical optimization , computer science , mathematical analysis , differential algebraic equation , geometry , evolutionary biology , artificial intelligence , aerospace engineering , economic growth , engineering , economics , biology , paleontology , machine learning
This research proposes the derivation of a class of hybrid methods for solution of second order initial value problems (IVPs) in block mode. Continuous linear multistep method of two cases with step number k = 4 is developed by interpolating the basis function at certain grid points and collocating the differential system at both grid and off-grid points. The basic properties of the method including order, error constant, zero stability, consistency and convergence were investigated. In order to examine the accuracy of the methods, some differential problems of order two were solved and results generated show a better performance when comparison is made with some current methods.Keywords- Block Method, Hybrid Points, Initial Value Problems, Power Series, Second Order