Search

In this paper, the Rational Jacobi (RJ) collocation method is proposed to approximate the solution of the boundary layer flow of an Eyring-Powell fluid over a stretching sheet. This equation is nonlinear and by applying Quasilinearization method (QLM), the equation is converted into a sequence of linear ordinary differential equations (ODE) converging to the solution of the nonlinear equation. Unlike other methods, instead of truncation in domain, the infinity condition is satisfied implicitly. As a result, using the proposed method, the model is converted to a system of linear algebraic equations. The effect of different parameters on the velocity profile is also presented., Comment: 20 pages, 14 figure

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.

In this paper a numerical meshless method for solving the radiative transfer equations in a slab medium with an isotropic scattering is considered. The method is based on radial basis functions to approximate the solution of an integral-partial differential equation by using collocation method. For this purpose different applications of RBFs are used. To this end the numerical solutions are obtained without any mesh generation into the domain of the problems. The results of numerical experiments are compared with the existing results in illustrative examples to confirm the accuracy and efficiency of the presented scheme. Also the norm of the residual functions are obtained to show the convergence of the method.

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.

Graphics Processing Units (GPUs) are high performance co-processors originally intended to improve the use and quality of computer graphics applications. Once, researchers and practitioners noticed the potential of using GPU for general purposes, GPUs applications have been extended from graphics applications to other fields. The main objective of this paper is to evaluate the impact of using GPU in solution of the transient diffusion type equation by parallel and stable group explicit finite difference method and encourage the researchers in this field to immigrate from implementing their algorithms in CPU to the GPU emerging world. For comparing them, we implemented the method in both GPU and CPU (multi-core) programming context. Moreover, we proposed an optimal synchronization arrangement for the implementation pseudo-code. Also, the interrelation of GPU parallel programming and initializing the algorithm variables were discussed, taking advantage of numerical experiences. The GPU-approach results are faster than those obtained from a much expensive parallel 8-thread CPU-based programming. The GPU used in this paper, is an ordinary old laptop GPU (GT 335M, launched at 2010) and is accessible for everyone and the newer generations of GPU (as discussed in paper) have even more performance priority over the similar-price GPUs. Then, the results are expected to encourage the entire research society to take advantage of GPUs and improve the time efficiency of their studies.

The objective of this paper is to apply the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs versus ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs and the differential equations solved by them do not have high-degree nonlinearity and the reported results are not regarded as appropriate criteria for the excellence of the new method. So, we chose Emden-Fowler type differential equations and solved them by this method. To confirm the accuracy of the new method and to show the preeminence of EOMs versus OOMs, the norm1 of the residual and error function of both methods are evaluated for multiple $m$ values, where $m$ is the degree of the Bernstein polynomials. We reported the results in form of plots to illustrate the error convergence of both methods to zero and also to show the primacy of the new method versus OOMs. The obtained results have demonstrated the increased accuracy of the new method.

In this paper two common collocation approaches based on radial basis functions have been considered; one be computed through the integration process (IRBF) and one be computed through the differentiation process (DRBF). We investigated the two approaches on natural convection heat transfer equations embedded in porous medium which are of great importance in the design of canisters for nuclear wastes disposal. Numerical results show that the IRBF be performed much better than the common DRBF, and show good accuracy and high rate of convergence of IRBF process., Comment: 23 pages, 4 figures; Published online in the journal of "Communications in Nonlinear Science and Numerical Simulation"

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"

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"

In this paper we propose a Lagrangian method for solving Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on a Modified generalized Laguerre functions Lagrangian method. The method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with some well-known results and show that the present solution is acceptable., Comment: 16 pages, 1 figures; Published online in the journal of "Acta Astronautica"

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"