Open AccessNumerical solution of third‐order boundary value problems by using a two‐step hybrid block method with a fourth derivative
Author(s) -
Rufai Mufutau Ajani,
Ramos Higinio
Publication year - 2021
Publication title -
computational and mathematical methods
Language(s) - English
Resource type - Journals
ISSN - 2577-7408
DOI - 10.1002/cmm4.1166
Subject(s) - mathematics , boundary value problem , collocation (remote sensing) , interpolation (computer graphics) , convergence (economics) , ordinary differential equation , block (permutation group theory) , third order , numerical analysis , derivative (finance) , linear multistep method , order (exchange) , mathematical analysis , differential equation , computer science , geometry , differential algebraic equation , philosophy , theology , finance , financial economics , economics , animation , computer graphics (images) , machine learning , economic growth
This article proposes a two‐step hybrid block method (TSHBM) with a fourth derivative for solving third‐order boundary value problems in ordinary differential equations. The mathematical formulation of the proposed approach depends on interpolation and collocation techniques. The order of convergence of the TSHBM is showed to be seventh‐order convergent and zero‐stable. A few numerical examples are given to evaluate its performance. Numerical outcomes show that the TSHBM scheme is more efficient than some existing numerical techniques.