A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area...

Article history: Received 17 June 2009 Received in revised form 4 October 2009 Accepted 13 October 2009 Available online 28 October 2009

A numerical simulation of the unsteady incompressible flow in the unit cavity is performed by using a Chebyshev-Tau approximation for the space variables. The high accuracy of the spectral methods and the condensed distribution of the Chebyshev-collocation points near the boundary enable us to obtain reliable results for high Reynolds numbers with a moderate number of modes. It is found that th...

A spectral method which uses a gauge method, as opposed to a projection method, to decouple the computation of velocity and pressure in the unsteady incompressible Navier–Stokes equations, is presented. Gauge methods decompose velocity into the sum of an auxilary field and the gradient of a gauge variable, which may, in principle, be assigned arbitrary boundary conditions, thus overcoming the i...

The normal mode model is important in computational atmospheric acoustics. It often used to compute the acoustic field under a time-independent single-frequency sound source. Its solution consists of set discrete modes radiating into upper atmosphere, usually related continuous spectrum. In this article, we present two spectral methods, Chebyshev-Tau and Chebyshev-Collocation solve for modes, c...

A mathematical investigation of a thermodynamical system linked with energy management and its impact on the environment, especially climate change, is presented in this study. In regard, numerical flow heat transfer hydromagnetic third-grade liquid through porous medium. The permeability medium electrical conductivity fluid are assumed to be temperature functions. appropriate formulations for ...

Poisson equation is frequently encountered in mathematical modeling for scientific and engineering applications. Fast Poisson numerical solvers for 2D and 3D problems are, thus, highly requested. In this paper, we consider solving the Poisson equation ∇2u = f(x, y) in the Cartesian domain Ω = [−1, 1] × [−1, 1], subject to all types of boundary conditions, discretized with the Chebyshev pseudosp...

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...