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Article
Publication date: 1 August 2002

M. Chrysos, F. Sanchez and Y. Cherruault

We show that Padé approximants considerably improve convergence of Adomian's decomposition. The power of the method proposed is demonstrated through two illustrative examples from…

Abstract

We show that Padé approximants considerably improve convergence of Adomian's decomposition. The power of the method proposed is demonstrated through two illustrative examples from the field of nonlinear optics.

Details

Kybernetes, vol. 31 no. 6
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 6 February 2017

S. Abbasbandy, Elyas Shivanian, K. Vajravelu and Sunil Kumar

The purpose of this paper is to present a new approximate analytical procedure to obtain dual solutions of nonlinear differential equations arising in mixed convection flow in a…

Abstract

Purpose

The purpose of this paper is to present a new approximate analytical procedure to obtain dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain. This method, which is based on Padé-approximation and homotopy–Padé technique, is applied to a model of magnetohydrodynamic Falkner–Skan flow as well. These examples indicate that the method can be successfully applied to solve nonlinear differential equations arising in science and engineering.

Design/methodology/approach

Homotopy–Padé method.

Findings

The main focus of the paper is on the prediction of the multiplicity of the solutions, however we have calculated multiple (dual) solutions of the model problem namely, mixed convection heat transfer in a porous medium.

Research limitations/implications

The authors conjecture here that the combination of traditional–Pade and Hankel–Pade generates a useful procedure to predict multiple solutions and to calculate prescribed parameter with acceptable accuracy as well. Validation of this conjecture for other further examples is a challenging research opportunity.

Social implications

Dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain.

Originality/value

In this study, the authors are using two modified methods.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 16 September 2013

Sima Samadpoor, Hadi Roohani Ghehsareh and Saeid Abbasbandy

The purpose of this paper is to obtain semi-analytical solutions of similarity solutions for the nano boundary layer flows with Navier boundary condition. The similarity solutions…

Abstract

Purpose

The purpose of this paper is to obtain semi-analytical solutions of similarity solutions for the nano boundary layer flows with Navier boundary condition. The similarity solutions of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface are investigated.

Design/methodology/approach

In this work, the governing partial differential equations are transformed to a nonlinear ordinary differential equation by using some proper similarity transformations. Then an efficient semi-analytical method, the Laplace Adomian decomposition method (LADM) is applied to obtain semi-analytical solutions of the similarity solutions in both of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface. To improve the accuracy and enlarges the convergence domain of the obtained results by the LADM, the study has combined it with Padé approximation.

Findings

Accuracy and efficiency of the presented method are illustrated and denoted through the tables and figures. Also the effects of the suction parameter λ and slip parameter K on the fluid velocity and on the tangential stress are investigated.

Originality/value

The similarity solutions of the governing partial differential equation are obtained analytically by using an efficient developed method, namely the Laplace Adomian decomposition-Padé method. The analytic solutions of nonlinear ordinary differential equation are constructed for both of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 29 July 2014

Buhe Eerdun, Qiqige Eerdun, Bala Huhe, Chaolu Temuer and Jing-Yu Wang

The purpose of this paper is to consider a steady two-dimensional magneto-hydrodynamic (MHD) Falkner-Skan boundary layer flow of an incompressible viscous electrically fluid over…

Abstract

Purpose

The purpose of this paper is to consider a steady two-dimensional magneto-hydrodynamic (MHD) Falkner-Skan boundary layer flow of an incompressible viscous electrically fluid over a permeable wall in the presence of a magnetic field.

Design/methodology/approach

The governing equations of MHD Falkner-Skan flow are transformed into an initial values problem of an ordinary differential equation using the Lie symmetry method which are then solved by He's variational iteration method with He's polynomials.

Findings

The approximate solution is compared with the known solution using the diagonal Pad’e approximants and the geometrical behavior for the values of various parameters. The results reveal the reliability and validity of the present work, and this combinational method can be applied to other nonlinear boundary layer flow problems.

Originality/value

In this paper, an approximate analytical solution of the MHD Falkner-Skan flow problem is obtained by combining the Lie symmetry method with the variational iteration method and He's polynomials.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 January 2014

Yasir Khan

This paper aims to suggest a novel modified Laplace decomposition method (MLDM) for MHD flow over a non-linear stretching sheet with slip condition by suitable choice of an…

Abstract

Purpose

This paper aims to suggest a novel modified Laplace decomposition method (MLDM) for MHD flow over a non-linear stretching sheet with slip condition by suitable choice of an initial solution.

Design/methodology/approach

The governing partial differential equations are converted into dimensionless non-linear ordinary differential equation by similarity transformation, which is solved by MLDM. The method is based on the application of Laplace transform to boundary layers in fluid mechanics. The non-linear term can be easily handled by the use of He's polynomials.

Findings

The series solution of the MHD flow of an incompressible viscous fluid over a non-linear stretching sheet subject to slip condition is obtained. An excellent agreement between the MLDM and HPM is achieved. Convergence of the obtained series solution is properly checked by using the ratio test.

Practical implications

Stretching surface is an important type of flow occurring in a number of engineering processes such as heat-treated materials travelling between a feed roll and a wind up roll, aerodynamic extrusion of plastic sheets, glass fiber and paper production, cooling of an infinite metallic plate in a cooling path, manufacturing of polymeric sheets are few examples of flow due to stretching surfaces. This work provides a very useful source of information for researchers on this subject.

Originality/value

Such flow analysis is even not available yet for the hydrodynamic fluid. The series solution for MHD boundary layer problem with slip condition by means of MLDM is yet not available in the literature.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 17 August 2012

M.M. Rashidi and E. Erfani

The purpose of this paper is to consider the thermal‐diffusion and diffusion‐thermo effects on combined heat and mass transfer of a steady magnetohydrodynamic (MHD) convective and…

Abstract

Purpose

The purpose of this paper is to consider the thermal‐diffusion and diffusion‐thermo effects on combined heat and mass transfer of a steady magnetohydrodynamic (MHD) convective and slip flow due to a rotating disk with viscous dissipation and Ohmic heating. The main goal of the present study is to find the approximate analytic solutions by the combination of the DTM and the Padé approximants for this problem.

Design/methodology/approach

A new method, namely the DTM‐Padé technique, which is a combination of the differential transform method and the Padé approximation, is employed.

Findings

Graphical results for fluids of medium molecular weight (H2, air) are presented to investigate influence of the slip parameter, magnetic field parameter M, Eckert Ec, Schmidt Ec, Dufour Du and Soret Sr numbers on the profiles of the dimensionless velocity, temperature and concentration distributions. In order to show the effectiveness of the DTM‐Padé, the results obtained from the DTM‐Padé are compared with available solutions obtained using shooting method to generate the numerical solution.

Originality/value

This technique (DTM‐Padé) is extended to give solutions for nonlinear differential equations with boundary conditions at the infinity.

Details

Engineering Computations, vol. 29 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 3 August 2012

Vedat Suat Erturk, Ahmet Yıldırım, Shaher Momanic and Yasir Khan

The purpose of this paper is to propose an approximate method for solving a fractional population growth model in a closed system. The fractional derivatives are described in the…

Abstract

Purpose

The purpose of this paper is to propose an approximate method for solving a fractional population growth model in a closed system. The fractional derivatives are described in the Caputo sense.

Design/methodology/approach

The approach is based on the differential transform method. The solutions of a fractional model equation are calculated in the form of convergent series with easily computable components.

Findings

The diagonal Padé approximants are effectively used in the analysis to capture the essential behavior of the solution.

Originality/value

Illustrative examples are included to demonstrate the validity and applicability of the technique.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 20 September 2011

Mohammad Mehdi Rashidi and Eemaeel Erfani

The purpose of this paper is to investigate the nano boundary‐layer flows over stretching surfaces with Navier boundary condition. This problem is mapped into the ordinary…

Abstract

Purpose

The purpose of this paper is to investigate the nano boundary‐layer flows over stretching surfaces with Navier boundary condition. This problem is mapped into the ordinary differential equation by presented similarity transformation. The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method. The authors consider two types of flows: viscous flows over a two‐dimensional stretching surface; and viscous flows over an axisymmetric stretching surface.

Design/methodology/approach

The governing equation is solved analytically by applying a newly developed method, namely the differential transform method (DTM)‐Padé technique that is a combination of the DTM and the Padé approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials.

Findings

Graphical results are presented to investigate influence of the slip parameter and the suction parameter on the normal velocity and on the lateral velocity. The obtained solutions, in comparison with the numerical solutions, demonstrate remarkable accuracy. It is predicted that the DTM‐Padé can have wide application in engineering problems especially for boundary‐layer problems.

Originality/value

The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method, namely the DTM‐Padé technique that is a combination of the DTM and the Padé approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 26 October 2012

Behrouz Raftari, Hojatollah Adibi and Ahmet Yildirim

The purpose of this work is to analytically examine the magnetohydrodynamic (MHD) Falkner‐Skan flow.

239

Abstract

Purpose

The purpose of this work is to analytically examine the magnetohydrodynamic (MHD) Falkner‐Skan flow.

Design/methodology/approach

The series solution is obtained using the Adomian decomposition method (ADM) coupled with Padé approximants.

Findings

Comparison of the present solutions is made with the results obtained by other applied methods and excellent agreement is noted.

Originality/value

In this work, the MHD Falkner‐Skan flow is examined analytically. The series solution is obtained using the ADM coupled with Padé approximants. Comparison of the present solutions is made with the results obtained by other applied methods and excellent agreement is noted.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 14 November 2008

Marissa Condon, Emira Dautbegovic and Tao Xu

The paper aims to propose several new approaches for the discrete‐time integration of stiff non‐linear differential equations.

Abstract

Purpose

The paper aims to propose several new approaches for the discrete‐time integration of stiff non‐linear differential equations.

Design/methodology/approach

The proposed approaches build on a method developed by the authors involving Padé approximates about each function sample. Both single‐ and multi‐step methods are suggested. The use of Richardson extrapolation is recommended for increasing efficiency.

Findings

The efficacy of the methods is shown using two examples and results are compared to a standard integration technique.

Originality/value

The paper shows that the methods are suitable for application in any field of science requiring efficient and accurate numerical solution of stiff differential equations.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 27 no. 6
Type: Research Article
ISSN: 0332-1649

Keywords

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