Abstract: Penetrative convection due to purely internal heating in a horizontal ferrofluid-saturated porous layer is examined by performing linear stability analysis. Four different types of heat supply functions are considered. The Darcy model is used to incorporate the effect of the porous medium. Numerical solutions are obtained by using the Chebyshev pseudospectral method, and the results a...

The Kidder problem is uxx + 2x(1 − αu)−1/2ux = 0 with u(0) = 1 and u(∞) = 0 where α ∈ [0, 1]. This looks challenging because of the square root singularity. We prove, however, that |u(x ;α) − erfc(x)| ≤ 0.046 for all x, α. Other very simple but very accurate curve fits and bounds are given in the text; |u(x ;α) − erfc(x + 0.15076x/(1 + 1.55607x2))| ≤ 0.0019. Maple code for a rational Chebyshev ...

The roundoo error analysis of several algorithms commonly used to compute the Fast Cosine Transform and the derivatives using the Chebyshev pseudospectral method are studied. We derive precise expressions for the algorithmic error, and using them we give new theoretical upper bounds and produce a statistical analysis. The results are compared with numerical experiments.

A study of the free vibration of Timoshenko beams and axisymmetric Mindlin plates is presented. The analysis is based on the Chebyshev pseudospectral method, which has been widely used in the solution of fluid mechanics problems. Clamped, simply supported, free and sliding boundary conditions of Timoshenko beams are treated, and numerical results are presented for different thickness-to-length ...

The problem of magnetohydrodynamic flow and heat transfer of a viscous, incompressible, and electrically conducting fluid past a semi-infinite unsteady stretching sheet is analyzed numerically. The problem was studied under the effects of Hall currents, variable viscosity, and variable thermal diffusivity. Using a similarity transformation, the governing fundamental equations are approximated b...

We develop a sparse grid spectral element method using nodal bases on Chebyshev-Gauss-Lobatto points for multi-dimensional elliptic equations. Since the quadratures based on sparse grid points do not have the accuracy of a usual Gauss quadrature, we construct the mass and stiffness matrices using a pseudo-spectral approach, which is exact for problems with constant coefficients and uniformly st...

In this paper, a Chebyshev spectral collocation domain decomposition (DD) semidiscretization by using a grid mapping, derived by Kosloff and Tal-Ezer in space is applied to the numerical solution of the generalized Burger’s–Huxley (GBH) equation. To reduce roundoff error in computing derivatives we use the above mentioned grid mapping. In this work, we compose the Chebyshev spectral collocation...

In this paper, a super spectral viscosity method using the Chebyshev differential operator of high order Ds = ( √ 1− x2∂x) is developed for nonlinear conservation laws. The boundary conditions are treated by a penalty method. Compared with the second-order spectral viscosity method, the super one is much weaker while still guaranteeing the convergence of the bounded solution of the Chebyshev–Ga...

In this work, we first reformulate the unsteady flow of gas through a porous medium problem in [0,+∞) to a problem in [-1,1] by variable transformation μ = (x-s)/(x+s), and using spectral collocation method based on Chebyshev polynomials to approximate the resulting problem. The comparison of the results obtained by this method with results obtained by other methods shows that this method provi...