In this paper, we derive an efficient spectral collocation algorithm to solve numerically the
nonlinear complex generalized Zakharov system (GZS) subject to initial-boundary …

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 …

An efficient technique, called pseudo-Galerkin, is performed to approximate some types of
linear/nonlinear BVPs. The core of the performance process is the two well-known weighted …

Shifted Legendre polynomials (SLPs) with the Riemann–Liouville fractional integral operator
have been used to create a novel fractional integration tool. This tool will be called the …

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 …

In this study, we solve some widely-used model problems consisting of linear, nonlinear
differential and integral equations, employing Dickson polynomials with the parameter-α and …

This paper presents a study of the performance of the Galerkin method using Legendre
basis functions for solving linear Fredholm integro-differential problems. Convergence and …

In this paper, the classical collocation method has been revisited and modified by using the
Chebyshev polynomials for solving nonlinear differential equations. Linear and nonlinear …

In this paper, an improved Bessel collocation method (IBCM) based on the residual
correction technique is presented to solve the high-order linear Volterra integro-differential …

In this paper, we proposed a new operational matrix of differentiation using CAS wavelets.
By aid of these matrices, CAS wavelets method (CASWM) is developed for the Integro …