A new class of polynomial functions equipped with a parameter

Abstract

In this study, a new class of polynomial functions although equipped with a parameter is introduced. This class can be employed for computational solution of linear or non-linear functional equations, including ordinary differential equations or integral equations. The extra parameter permits us to obtain more accurate results. In the present paper, a number of numerical examples show the ability of this class of polynomial functions.

Numerical Approach for Solving the Fractional Pantograph Delay Differential Equations

“…It is due to the simple application of them. Recently, a new class of polynomials equipped with an auxiliary parameter has been introduced by the first author in [35] and some applications of it have been shown in [36][37][38][39]. is class is introduced as follows.…”

Numerical solution to the Falkner-Skan equation: a novel numerical approach through the new rational a-polynomials

“…Definition [28] Assume that a is a constant parameter and A 0 (z) = 1. The a-polynomials as a combination of the Chebyshev polynomials of the second kind, U n (z), are defined by…”

“…See Refs. [24] and [28] for more properties. By changing the variable z = η−L η+L for η ∈ [0, +∞), in which L is an arbitrary large positive number and will be chosen later, the following new rational a-polynomials are obtained from Eq.…”