We develop direct solution techniques for solving high-order differential equations with
constant coefficients using the spectral tau method. The spatial approximation is based on …

In this research paper, we address the time-fractional heat conduction equation in one
spatial dimension, subject to nonlocal conditions in the temporal domain. To tackle this …

In this work, first, a family of fourth‐order methods is proposed to solve nonlinear equations.
The methods satisfy the Kung‐Traub optimality conjecture. By developing the methods into …

Herein, we construct an explicit modal numerical solver based on the spec-tral Petrov–
Galerkin method via a specific combination of shifted Cheby-shev polynomial basis for …

This paper presents a numerical strategy for solving the nonlinear time fractional Burgers's
equation (TFBE) to obtain approximate solutions of TFBE. During this procedure, the …

This article is dedicated to propose a spectral solution for the non-linear Fitzhugh–Nagumo
equation. The proposed solution is expressed as a double sum of basis functions that are …

This study presents a new efficient collocation approach to handle the nonlinear generalized
fractional Riccati equation. The linearization formula of the product of two shifted Chebyshev …

In this article, we introduce a novel spectral algorithm utilizing Fibonacci polynomials to
numerically solve both linear and nonlinear integro-differential equations with fractional …

The principle objective of this article is to introduce and investigate a type of orthogonal
polynomials that are written as combinations of Legendre polynomials. This kind of …

This work tackles the mathematical modeling of buckling problem to obtain their critical
loads in tapered columns subjected to concentrated and axial distributed loads. The …