This study presents the Fourier-Gegenbauer Integral-Galerkin (FGIG) method, a novel and
efficient numerical framework for solving the one-dimensional advection-diffusion equation …

A numerical approach to approximate the nonlinear Burgers' equation solution is presented
in this article. By temporally discretizing the problem using the Crank-Nicolson scheme, we …

In our investigation, we apply the spectral homotopy analysis method (SHAM) to tackle the
numerical resolution of the Duffing and Van Der Pol equations. We compute the numerical …

The article focuses on developing a numerical method for solving the advection-diffusion-
reaction equation using a combination of approximation techniques. Topics include the …

The aim of this work is to study various problems of mathematical equations using spectral
methods. It develops four numerical techniques suitable for every studied problem and …