Open AccessNew Seven-Step Numerical Method for Direct Solution of Fourth Order Ordinary Differential Equations
Author(s) -
Zurni Omar,
John Olusola Kuboye
Publication year - 2016
Publication title -
journal of mathematical and fundamental sciences/journal of mathematical and fundamental siences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.216
H-Index - 12
eISSN - 2337-5760
pISSN - 2338-5510
DOI - 10.5614/j.math.fund.sci.2015.48.2.1
Subject(s) - collocation method , mathematics , ordinary differential equation , collocation (remote sensing) , interpolation (computer graphics) , orthogonal collocation , numerical methods for ordinary differential equations , convergence (economics) , numerical stability , explicit and implicit methods , mathematical analysis , linear multistep method , order of accuracy , consistency (knowledge bases) , power series , differential equation , numerical analysis , differential algebraic equation , computer science , geometry , economics , animation , computer graphics (images) , machine learning , economic growth
A new numerical method for solving fourth order ordinary differential equations directly is proposed in this paper. Interpolation and collocation were employed in developing this method using seven steps. The use of the approximated power series as an interpolation equation was adopted in deriving the method. The basic properties of the new method such as zero-stability, consistency, convergence and order are established. The numerical results indicate that the new method gives better accuracy than the existing methods when it is applied to fourth ordinary differential equations