An approximate solution of the MHD Falkner-Skan flow by Hermite functions pseudospectral method

Based on a new approximation method, namely pseudospectral method, a solution for the three order nonlinear ordinary differential laminar boundary layer Falkner-Skan equation has been obtained on the semi-infinite domain. The proposed approach is equipped by the orthogonal Hermite functions that have perfect properties to achieve this goal. This method solves the problem on the semi-infinite domain without truncating it to a finite domain and transforming domain of the problem to a finite domain. In addition, this method reduces solution of the problem to solution of a system of algebraic equations. We also present the comparison of this work with numerical results and show that the present method is applicable.Comment: 15 pages, 4 figures; Published online in the journal of "Communications in Nonlinear Science and Numerical Simulation

Numerical approximations for population growth model by Rational Chebyshev and Hermite Functions collocation approach: A comparison

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 reduces the solution of this problem to the solution of a system of algebraic equations. We also compare these methods with some other numerical results and show that the present approach is applicable for solving nonlinear integro-differential equations.Comment: 18 pages, 5 figures; Published online in the journal of "Mathematical Methods in the Applied Sciences

Some new uniform approximate analytical representations of the Blasius function.

New uniform approximations of the Blasius velocity profile and Blasius function are developed from existing rational approximations of the Blasius velocity profile and of the Blasius function itself. Essentially, the existing rational approximations are rescaled (when necessary) and one of two methodologies [1, 11] is applied to the rescaled rational approximations to determine corresponding uniform approximations to the Blasius velocity profile and Blasius function. A brief discussion is presented on the merits of the results

On compact uniform analytical approximations to the Blasius Velocity profile.

It is shown that approximate analytical representations of the Blasius function may be developed by using the error function, erf (ax), for positive constant a, as a basic compact approximate form for the derivative of the Blasius function, that is, the dimensionless velocity profile for the Blasius problem. This compact approximate analytical representation of the Blasius velocity function is then refined by the addition, following Savaş [13], of another parameter, to obtain further approximate analytical representations of the Blasius function

An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method

In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value problems. The proposed approach is based on a Hermite function collocation (HFC) method. To illustrate the reliability of the method, some special cases of the equations are solved as test examples. The new method reduces the solution of a problem to the solution of a system of algebraic equations. Hermite functions have prefect properties that make them useful to achieve this goal. We compare the present work with some well-known results and show that the new method is efficient and applicable.Comment: 34 pages, 13 figures, Published in "Computer Physics Communications

Influence of inclined magnetic field and chemical reaction on the entropy generation of Blasius and Sakiadis flows

This work considers the well-known laminar boundary layer flows; about a flat-plate in a uniform stream of fluid (Blasius flow) and about a moving plate in a quiescent am- bient fluid (Sakiadis flow) both under a convective surface boundary condition. Entropy generation due to the effect of angle of inclination, magnetic parameter, chemical reaction parameter and Schmidt number on the flows is investigated. The third order partial dif- ferential equations governing the flows are reduced to ordinary differential equations by suitable similarity variables. The obtained equations are tackled by the Runge-Kutta fourth order method with shooting technique and the results are employed to calculate entropy generation. The solution of Blasius flow is compared with the works in literature and are found to be in excellent agreement. Entropy generation can be minimized by increasing the magnetic parameter (M), chemical reaction parameter (R) and Schmidt number (Sc) for Blasius flow. Magnetic parameter reduces entropy generation for Sakiadis flow while other parameters such as angle of inclination, chemical reaction parameter and Schmidt number boost fluid irreversibility