Numerical Performances of Two Orthogonal Polynomials in the Tau Method for Solutions of Ordinary Differential Equations

Abstract

In this work, efforts are made at comparing the numerical effectiveness of the two most accurate orthogonal polynomials; Chebyshev and Legendre polynomials. Although the two have different weight functions, but they most time give close results especially when they are considered in the same interval. This work has therefore used the two polynomials, within the same interval, as bases functions in the Ortiz’s Recursive Formulation of Lanczos’ Tau method. Numerical experiments show that the two are very accurate.

Keywords: Tau System, Canonical Polynomials, Legendre Polynomials, Tau Approximant