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 …

Herein, new orthogonal polynomials have been generated from shifted Chebyshev
polynomials that fulfill a given set of homogeneous boundary conditions and the necessary …

Herein, modified orthogonal polynomials are introduced. These polynomials are generated
from the second kind of shifted Chebyshev polynomials on the interval [α, β]. The operational …

This paper will focus on determining the approximate numerical solutions for several types
of linear and nonlinear Ordinary differential equations. This solution is based on the direct …

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 …

The intention of this analysis is to declare and demonstrate the complete foundational
theorem of existence and uniqueness for fractional conformable initial value time-delayed …

The purpose of this study is to introduce a computational method for solving the two-
dimensional optimal control problem of the large membrane vibration equation of fractional …