In this study, we propose to derive an accurate numerical procedure to solve the mathematical model which describes the electrical R-L circuit composed of resistors and inductors driven by a voltage of current source, which is the fractional-order model for the electrical RL-circuit. Our study depends on the spectral collocation method via the useful properties of the Chebyshev polynomials of the third-kind. Some theorems about the convergence analysis are given. The study concludes by comparing the resulting approximate solutions of the proposed model with the exact solution in the classical case. Illustrative graphical and numerical analysis of the derived results are also included in this study.

This paper present an accurate numerical algorithm to solve the space fractional-order Fisher’s equation where the derivative operator is described in the Caputo derivative sense. In the presented discretization process, first we use the compact nite difference (CFD) to occur a semi-discrete in time derivative, and implement the Chebyshev spectral collocation method (CSCM) of the third-kind to discretize the spatial fractional derivative. The presented method converts the studied problem to be a system of algebraic equations which can be easily solved. To study the convergence and stability analysis, some theorems are given with their profs. A numerical simulation is given to test the accuracy and the applicability of our presented algorithm.

An efficient numerical method is presented in this study to discuss the effects of variable heat flux, viscous dissipation and the slip velocity on the viscous Casson flow and heat transfer due to an unsteady stretching sheet taking into account the influence of heat generation or absorption. Industrially, this type of fluid can describe the flow of blood in an industrial artery, which can be polished by a material governing the blood flow. The spectral collocation method based on Chebyshev polynomials of the third-kind is employed to solve the resulting system of ordinary differential equations which describe the problem. Influence of the parameters governing the flow and heat transfer such as unsteadiness parameter, slip velocity parameter, Casson parameter, local Eckert number, heat generation parameter and the Prandtl number are discussed and presented through tables and graphs. Also, the local skin-friction coefficient and the local Nusselt number at the stretching sheet are computed and discussed. Finally, the results show that the given procedure is an easy and efficient tool to investigate the solution of such fluid models.