The pseudo-spectral method is used as a technique to employ the first derivative of the well-
known Legendre polynomials (FDLs) as novel basis functions. Then, the FDLs Gauss …

Herein, a pure shifted Jacobi–Galerkin (SJG) method is offered for handling linear two-
dimensional space-time diffusion and telegraph equations but by considering their …

This paper will present a highly efficient technique for solving linear and nonlinear
differential equations. We will use the second derivative of Legendre polynomials as new …

The aim of this paper is to use the second derivative of Chebyshev polynomials (SDCHPs)
as basis functions for solving linear and nonlinear boundary value problems (BVPs). Then …

A new form of basis functions structures has been constructed. These basis functions
constitute a mix of Chebyshev polynomials and Legendre polynomials. The main purpose of …

This research work aims to theoretically examine the influence of various factors on the three-
dimensional nanofluid flow. The study includes parameters such as temperature ratio …

In this paper, Chebyshev polynomial derivative-based spectral schemes are constricted for
solving linear and non-linear ordinary differential equations. Linearization relation and some …

This paper presents a method for optimizing photovoltaic (PV) system placement in
distribution systems using the Newton-Raphson (NR) method with MATLAB code and E-Tap …

This paper established a functional design of the spectral Tau method (STM) upon the first
derivatives of Chebyshev polynomials (FDCHPs). A new linearization relation has been …