Relative in Numerical Performance of Certain Polynomials in Tau Method

Abstract

This paper examines the order of numerical usefulness of the four kinds of Chebyshev polynomials, especially in the differential formulation of the Lanczos’ Tau method. Their practical applications on selected numerical problems, which are constant and variable coefficients, homogeneous and nonhomogeneous problems of varied orders, showed correlation between the accuracy first and fourth kinds. The second kind was next in performance, while the third kind performed least.