This research aims to assemble two methodical spectral Legendre's derivative algorithms to
numerically attack the Lane-Emden, Bratu's, and singularly perturbed type equations. We …

Through the current article, a numerical technique to obtain an approximate solution of one-
dimensional linear hyperbolic partial differential equations is implemented. A certain …

This paper is devoted to the model of Lassa hemorrhagic fever (LHF) disease in pregnant
women. This disease is a biocidal fever and epidemic. LHF disease in pregnant women has …

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 …

A new differentiation technique, fractional pseudospectral shifted Legendre differentiation
matrices (FSL D-matrices), was introduced. It depends on shifted Legendre polynomials …

This paper is devoted to developing spectral solutions for the nonlinear fractional Klein–
Gordon equation. The typical collocation method and the tau method are employed for …

We introduce new differentiation matrices based on the pseudospectral collocation method.
Monic Chebyshev polynomials (MCPs) were used as trial functions in differentiation …

In this paper, our target is to implement and analyze numerical algorithms for the numerical
solutions of initial and boundary third-order singular-type equations, and in particular the …

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 …

A new numerical scheme based on the tau spectral method for solving the linear hyperbolic
telegraph type equation is presented and implemented. The derivation of this scheme is …