A Numerical Method Based on Legendre Differentiation Matrices for Higher Order Odes

Abstract

This paper introduces a new method to obtain the spectral accuracy solutions to higher order differential equations and singularly perturbed boundary value problems (BVPs). Legendre polynomials (LPs) Pn (x) have been used and involved in straightforward implementation method. Asymptotic upper bound on the Legendre coefficients for the kt h derivatives are presented. Also, We detect the roundoff error effect in the Legendre matrices. The superiority of the suggested method became evident through some examples and applications. © 2020 NSP Natural Sciences Publishing Cor.