Approximate Solution of An Ordinary Differential And Integral Equations Using Collocation Method Based On Hermite Legendre Polynomials
No Thumbnail Available
Date
2021-03
Journal Title
Journal ISSN
Volume Title
Publisher
Faculty of Natural and Applied Sciences, Umaru Musa yar'adua University, Kastina
Abstract
In this work, we employed an approximate solution of second and third-order Initial Value Problems (IVPs) in
Ordinary Differential Equations (ODEs) by utilizing a standard collocation method based on Hermite and Legendre
polynomials. The ODEs were first converted to integral equations and the basis function was substituted to obtain a
set of linear algebraic which then form equations that were solved via maple 2021. Comparisons were made with the
two trial solutions mentioned above in terms of errors obtained. Numerical examples were given to illustrate the
performance of the method for various orders. However, the Hermite polynomial basis exhibits better accuracy over
the Legendre polynomials in some results as can be seen from the tables of errors presented.
Description
Keywords
Citation
Hermite Polynomial, Initial Value program, integral Equation, Legendre Polynomial, Standard Collocation Method.