In this paper, the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linearly stretching sheet is solved using the combination of the quasilinearization method and the Fractional order of Rational Chebyshev function (FRC) collocation method on a semi-infinite domain. The quasilinearization method converts the equation into a sequence of linear equations then, using the FRC coll...

Lane-Emden equation is a nonlinear singular equation that plays an important role in the astrophysics. In this paper, we have applied the collocation method based on rational Chebyshev functions to solve Lane-Emden type equations. The method reduces solving the nonlinear ordinary differential equation to solving a system of nonlinear algebraic equations. The comparison of the results with the o...

This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF) collocation approach to solve the Volterra’s model for population growth of a species within a closed system. This model is a nonlinear integro-differential equation where the integral term represents the effect of toxin. This approach is based on orthogonal functions which will be defined. The collocation method redu...

Abstract This work is devoted to the analysis of linear temporal stability a laminar dynamic boundary layer on horizontal porous plane plate. The basic flow assumed be and two-dimensional. velocity profiles are obtained by numerically solving Blasius equation using Runge-Kutta method. perturbations these solutions expressed in form three-dimensional Tollmien-Schlichting waves. formulation probl...

An efficient treatment is developed for the Schrödinger equation with a class of local absorbing boundary conditions, which are obtained by high order Padé expansions. These boundary conditions are significant in the simulation of open quantum devices. Based on the finite difference approximation in the interior domain, we construct a spectral collocation layer on the cell near the artificial b...

This paper concerns the iterative solution of the linear system arising from the Chebyshev–collocation approximation of second-order elliptic equations and presents an optimal multigrid preconditioner based on alternating line Gauss–Seidel smoothers for the corresponding stiffness matrix of bilinear finite elements on the Chebyshev–Gauss–Lobatto grid.  2000 IMACS. Published by Elsevier Science...

The spectral collocation method for solving two-point boundary value problems second order differential equations is implemented, based on representing the solution as an expansion in Chebyshev polynomials. approach allows a stable calculation of both representation and its pointwise any required grid definition domain equation additional conditions multipoint problem. For effective constructio...

Problem statement: Not all differential equations can be solved analytically, to overcome this problem, there is need to search for an accurate approximate solution. Approach: The objective of this study was to find an accurate approximation technique (scheme) for solving linear differential equations. By exploiting the Trigonometric identity property of the Chebyshev polynomial, we developed a...