Open AccessA New L-Stable Third Derivative Hybrid Method for Solving First Order Ordinary Differential Equations
Author(s) -
Lawrence Osa Adoghe
Publication year - 2021
Publication title -
asian research journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-477X
DOI - 10.9734/arjom/2021/v17i630310
Subject(s) - mathematics , linear multistep method , ordinary differential equation , collocation method , orthogonal collocation , collocation (remote sensing) , convergence (economics) , interpolation (computer graphics) , derivative (finance) , power series , stability (learning theory) , mathematical analysis , block (permutation group theory) , differential equation , computer science , differential algebraic equation , geometry , animation , computer graphics (images) , machine learning , economic growth , financial economics , economics
In this paper, an L-stable third derivative multistep method has been proposed for the solution of stiff systems of ordinary differential equations. The continuous hybrid method is derived using interpolation and collocation techniques of power series as the basis function for the approximate solution. The method consists of the main method and an additional method which are combined to form a block matrix and implemented simultaneously. The stability and convergence properties of the block were investigated and discussed. Numerical examples to show the efficiency and accuracy of the new method were presented.