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Fatemeh Baharifard - One of the best experts on this subject based on the ideXlab platform.

  • Solving a laminar boundary layer Equation with the rational Gegenbauer functions
    Applied Mathematical Modelling, 2013
    Co-Authors: Kourosh Parand, Mehdi Dehghan, Fatemeh Baharifard
    Abstract:

    Abstract In this paper, a collocation method using a new weighted orthogonal system on the half-line, namely the rational Gegenbauer functions, is introduced to solve numerically the third-order nonlinear differential Equation, af ‴ + ff ″ = 0 , where a is a constant parameter. This method solves the problems on semi-infinite domain without truncating it to a finite domain and transforming the domain of the problems to a finite domain. For a = 2 , the Equation is the well-known Blasius Equation, which is a laminar viscous flow over a semi-infinite flat plate. We solve this Equation by considering 1 ⩽ a ⩽ 2 and compare the new results with the established results to show the efficiency and accuracy of the new method.

  • A new Reliable Numerical Algorithm Based on the First Kind of Bessel Functions to Solve Prandtl–Blasius Laminar Viscous Flow over a Semi-Infinite Flat Plate
    Zeitschrift für Naturforschung A, 2012
    Co-Authors: Kourosh Parand, Mehran Nikarya, Jamal Amani Rad, Fatemeh Baharifard
    Abstract:

    In this paper, a new numerical algorithm is introduced to solve the Blasius Equation, which is a third-order nonlinear ordinary differential Equation arising in the problem of two-dimensional steady state laminar viscous flow over a semi-infinite flat plate. The proposed approach is based on the first kind of Bessel functions collocation method. The first kind of Bessel function is an infinite series, defined on R and is convergent for any x2R. In this work, we solve the problem on semi-infinite domain without any domain truncation, variable transformation basis functions or transformation of the domain of the problem to a finite domain. This method reduces the solution of a nonlinear problem to the solution of a system of nonlinear algebraic Equations. To illustrate the reliability of this method, we compare the numerical results of the present method with some well-known results in order to show the applicability and efficiency of our method.

Kourosh Parand - One of the best experts on this subject based on the ideXlab platform.

  • Solving a laminar boundary layer Equation with the rational Gegenbauer functions
    Applied Mathematical Modelling, 2013
    Co-Authors: Kourosh Parand, Mehdi Dehghan, Fatemeh Baharifard
    Abstract:

    Abstract In this paper, a collocation method using a new weighted orthogonal system on the half-line, namely the rational Gegenbauer functions, is introduced to solve numerically the third-order nonlinear differential Equation, af ‴ + ff ″ = 0 , where a is a constant parameter. This method solves the problems on semi-infinite domain without truncating it to a finite domain and transforming the domain of the problems to a finite domain. For a = 2 , the Equation is the well-known Blasius Equation, which is a laminar viscous flow over a semi-infinite flat plate. We solve this Equation by considering 1 ⩽ a ⩽ 2 and compare the new results with the established results to show the efficiency and accuracy of the new method.

  • A new Reliable Numerical Algorithm Based on the First Kind of Bessel Functions to Solve Prandtl–Blasius Laminar Viscous Flow over a Semi-Infinite Flat Plate
    Zeitschrift für Naturforschung A, 2012
    Co-Authors: Kourosh Parand, Mehran Nikarya, Jamal Amani Rad, Fatemeh Baharifard
    Abstract:

    In this paper, a new numerical algorithm is introduced to solve the Blasius Equation, which is a third-order nonlinear ordinary differential Equation arising in the problem of two-dimensional steady state laminar viscous flow over a semi-infinite flat plate. The proposed approach is based on the first kind of Bessel functions collocation method. The first kind of Bessel function is an infinite series, defined on R and is convergent for any x2R. In this work, we solve the problem on semi-infinite domain without any domain truncation, variable transformation basis functions or transformation of the domain of the problem to a finite domain. This method reduces the solution of a nonlinear problem to the solution of a system of nonlinear algebraic Equations. To illustrate the reliability of this method, we compare the numerical results of the present method with some well-known results in order to show the applicability and efficiency of our method.

  • Modified generalized Laguerre function Tau method for solving laminar viscous flow: The Blasius Equation
    International Journal of Numerical Methods for Heat & Fluid Flow, 2010
    Co-Authors: Kourosh Parand, Mehdi Dehghan, A. Taghavi
    Abstract:

    Purpose – The purpose of this paper is to propose a Tau method for solving nonlinear Blasius Equation which is a partial differential Equation on a flat plate.Design/methodology/approach – The operational matrices of derivative and product of modified generalized Laguerre functions are presented. These matrices together with the Tau method are then utilized to reduce the solution of the Blasius Equation to the solution of a system of nonlinear Equations.Findings – The paper presents the comparison of this work with some well‐known results and shows that the present solution is highly accurate.Originality/value – This paper demonstrates solving of the nonlinear Blasius Equation with an efficient method.

  • Sinc-collocation method for solving the Blasius Equation
    Physics Letters A, 2009
    Co-Authors: Kourosh Parand, Mehdi Dehghan, A. Pirkhedri
    Abstract:

    Sinc-collocation method is applied for solving Blasius Equation which comes from boundary layer Equations. It is well known that sinc procedure converges to the solution at an exponential rate. Comparison with Howarth and Asaithambi's numerical solutions reveals that the proposed method is of high accuracy and reduces the solution of Blasius' Equation to the solution of a system of algebraic Equations.

  • Rational scaled generalized Laguerre function collocation method for solving the Blasius Equation
    Journal of Computational and Applied Mathematics, 2009
    Co-Authors: Kourosh Parand, A. Taghavi
    Abstract:

    In this paper we propose, a collocation method for solving the Blasius Equation. The Blasius Equation is a third-order nonlinear ordinary differential Equation. This approach is based on a rational scaled generalized Laguerre function collocation method. We also present the comparison of this work with some well-known results and show that the present solution is accurate.

Mehdi Dehghan - One of the best experts on this subject based on the ideXlab platform.

  • Solving a laminar boundary layer Equation with the rational Gegenbauer functions
    Applied Mathematical Modelling, 2013
    Co-Authors: Kourosh Parand, Mehdi Dehghan, Fatemeh Baharifard
    Abstract:

    Abstract In this paper, a collocation method using a new weighted orthogonal system on the half-line, namely the rational Gegenbauer functions, is introduced to solve numerically the third-order nonlinear differential Equation, af ‴ + ff ″ = 0 , where a is a constant parameter. This method solves the problems on semi-infinite domain without truncating it to a finite domain and transforming the domain of the problems to a finite domain. For a = 2 , the Equation is the well-known Blasius Equation, which is a laminar viscous flow over a semi-infinite flat plate. We solve this Equation by considering 1 ⩽ a ⩽ 2 and compare the new results with the established results to show the efficiency and accuracy of the new method.

  • Modified generalized Laguerre function Tau method for solving laminar viscous flow: The Blasius Equation
    International Journal of Numerical Methods for Heat & Fluid Flow, 2010
    Co-Authors: Kourosh Parand, Mehdi Dehghan, A. Taghavi
    Abstract:

    Purpose – The purpose of this paper is to propose a Tau method for solving nonlinear Blasius Equation which is a partial differential Equation on a flat plate.Design/methodology/approach – The operational matrices of derivative and product of modified generalized Laguerre functions are presented. These matrices together with the Tau method are then utilized to reduce the solution of the Blasius Equation to the solution of a system of nonlinear Equations.Findings – The paper presents the comparison of this work with some well‐known results and shows that the present solution is highly accurate.Originality/value – This paper demonstrates solving of the nonlinear Blasius Equation with an efficient method.

  • Sinc-collocation method for solving the Blasius Equation
    Physics Letters A, 2009
    Co-Authors: Kourosh Parand, Mehdi Dehghan, A. Pirkhedri
    Abstract:

    Sinc-collocation method is applied for solving Blasius Equation which comes from boundary layer Equations. It is well known that sinc procedure converges to the solution at an exponential rate. Comparison with Howarth and Asaithambi's numerical solutions reveals that the proposed method is of high accuracy and reduces the solution of Blasius' Equation to the solution of a system of algebraic Equations.

  • modified rational legendre approach to laminar viscous flow over a semi infinite flat plate
    Chaos Solitons & Fractals, 2008
    Co-Authors: T Tajvidi, Mohsen Razzaghi, Mehdi Dehghan
    Abstract:

    Abstract A numerical method for solving the classical Blasius’ Equation is proposed. The Blasius’ Equation is a third order nonlinear ordinary differential Equation , which arises in the problem of the two-dimensional laminar viscous flow over a semi-infinite flat plane. The approach is based on a modified rational Legendre tau method. The operational matrices for the derivative and product of the modified rational Legendre functions are presented. These matrices together with the tau method are utilized to reduce the solution of Blasius’ Equation to the solution of a system of algebraic Equations. A numerical evaluation is included to demonstrate the validity and applicability of the method and a comparison is made with existing results.

Ishak Hashim - One of the best experts on this subject based on the ideXlab platform.

  • Solving directly third-order ODEs using operational matrices of Bernstein polynomials method with applications to fluid flow Equations
    Journal of King Saud University - Science, 2019
    Co-Authors: Sana’a Nazmi Khataybeh, Ishak Hashim, Mohammed Hamed Alshbool
    Abstract:

    Abstract In this paper, we adapt for the first time the operational matrices of Bernstein polynomials method for solving directly a class of third-order ordinary differential Equations (ODEs). This method gives a numerical solution by converting the Equation into a system of algebraic Equations which is solved directly. Applications of the present method to the famous Blasius Equation describing a boundary layer flow over a flat plate and third-order ODE for thin film flow are presented. Some numerical examples are also given to show the applicability of the method.

  • comments on a new algorithm for solving classical Blasius Equation by l wang
    Applied Mathematics and Computation, 2006
    Co-Authors: Ishak Hashim
    Abstract:

    Abstract In a recent paper, Wang [L. Wang, A new algorithm for solving classical Blasius Equation, Appl. Math. Comput. 157 (2004) 1–9.] employed the Adomian decomposition method (ADM) to solve numerically the famous Blasius Equation. The purpose of this note is to correct the numerical solution of Wang and to present an improved numerical solution using the ADM–Pade approach. The numerical result compares reasonably well with the result obtained from a shooting method.

Bohua Sun - One of the best experts on this subject based on the ideXlab platform.