This paper is focused on performing a new method for solving linear and nonlinear higher-
order boundary value problems (HBVPs). This direct numerical method based on spectral …

New modified shifted Chebyshev polynomials (MSCPs) have been constructed over the
interval [α, β]. These polynomials are utilized as basis functions with the application of the …

In this study, a spectral tau solution to the heat conduction equation is introduced. As basis
functions, the orthogonal polynomials, namely, the shifted fifth-kind Chebyshev polynomials …

This paper is dedicated to deriving novel formulae for the high‐order derivatives of
Chebyshev polynomials of the fifth‐kind. The high‐order derivatives of these polynomials …

The present work proposes a new, highly accurate and efficient computational technique for
numerical solution of a strongly nonlinear singular two-point boundary value problem which …

Load leveling problems and energy storage systems can be modeled in the form of Volterra
integral equations (VIE) with a discontinuous kernel. The Lagrange–collocation method is …

In this article, we propose new spectral solutions for odd-order two-point boundary value
problems. A numerical algorithm based on the use of collocation methods is implemented …

In this paper we consider some applications of Odd and Even Lidstone-type polynomial
sequences. In particular we deal with the Odd and Even Lidstone-type and the Generalized …

In this paper, we introduce new non-polynomial basis functions for spectral approximation of
time-fractional partial differential equations (PDEs). Different from many other approaches …

A new finite element approach is developed here for the modeling of boundary value
problems. In the present model, the finite element method (FEM) is reformulated by new …