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

A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions

In this paper, the fractional order of rational Bessel functions collocation method (FRBC) to solve Thomas-Fermi equation which is defined in the semi-infinite domain and has singularity at $x = 0$ and its boundary condition occurs at infinity, have been introduced. We solve the problem on semi-infinite domain without any domain truncation or transformation of the domain of the problem to a finite domain. This approach at first, obtains a sequence of linear differential equations by using the quasilinearization method (QLM), then at each iteration solves it by FRBC method. To illustrate the reliability of this work, we compare the numerical results of the present method with some well-known results in other to show that the new method is accurate, efficient and applicable

A new operational matrix based on Bernoulli polynomials

In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized to transform the differential equation to a matrix equation which corresponds to a system of algebraic equations with unknown Bernoulli coefficients. This method can be used for many problems such as differential equations, integral equations and so on. Numerical examples show the method is computationally simple and also illustrate the efficiency and accuracy of the method

A numerical study on reaction-diffusion problem using radial basis functions

In this paper, the collocation approach, based on the indirect radial basis functions on boundary value problems (IRBFB), is used to obtain a solution for the problem of a non-linear model of reaction-diffusion in porous catalysis pellets for the case of $n$th-order reaction. One of the boundaries of porous slab is impermeable and the other one is held at constant concentration. We applied this method through the integration process on the boundary value reaction-diffusion problem. The Thiele modulus thus measures the relative importance of the diffusion and reaction phenomena. Interestingly, for the large Thiele modulus the IRBFB offer a reasonable solution. Numerical results and findings obtained by the comparison with finite difference method, show a good accuracy and appropriate convergence rate of IRBFB process

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

Numerical Study on Wall Temperature and Surface Heat Flux Natural Convection Equations Arising in Porous Media by Rational Legendre Collocation Approach

Abstract: In this paper, a new powerful approach, called rational Legendre collocation method (RLC) is used to obtain the solution for nonlinear ordinary deferential equations that often appear in boundary layers problems arising in heat transfer. These kinds of the equations contain infinity boundary condition. The main objective is to reduce the solution of the problem to a solution of a system of algebraic equations, which do not require linearization and imposing the asymptotic condition transforming and physically unrealistic assumptions. Numerical results are compared with those of other methods, showing that the collocation method leads to more accurate results