%0 Journal Article
%T Modified Legendre Collocation Block Method for Solving Initial Value Problems of First Order Ordinary Differential Equations
%A Toyin Gideon Okedayo
%A Ayodele Olakiitan Owolanke
%A Olaseni Taiwo Amumeji
%A Muyiwa Philip Adesuyi
%J Open Access Library Journal
%V 5
%N 7
%P 1-15
%@ 2333-9721
%D 2018
%I Open Access Library
%R 10.4236/oalib.1104565
%X
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.
%K Block
%K Legendre Polynomials
%K Zero-Stable
%K Convergent
%U http://www.oalib.com/paper/5293638