TITLE:
Modified Legendre Collocation Block Method for Solving Initial Value Problems of First Order Ordinary Differential Equations
AUTHORS:
Toyin Gideon Okedayo, Ayodele Olakiitan Owolanke, Olaseni Taiwo Amumeji, Muyiwa Philip Adesuyi
KEYWORDS:
Block, Legendre Polynomials, Zero-Stable, Convergent
JOURNAL NAME:
Open Access Library Journal,
Vol.5 No.7,
July
6,
2018
ABSTRACT: In this paper, block procedure for some k-step linear multi-step methods, using the Legendre polynomials as the basis functions, is proposed. Discrete methods were given which were used in block and implemented for solving the initial value problems, being continuous interpolant derived and collocated at grid points. Some numerical examples of ordinary differential equations were solved using the derived methods to show their validity and the accuracy. The numerical results obtained show that the proposed method can also be efficient in solving such problems.