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1 – 20 of 45
Article
Publication date: 5 October 2012

Mehmet Merdan, Ahmet Yildirim and Ahmet Gökdoğan

The purpose of this paper is to show how an application of fractional two dimensional differential transformation method (DTM) obtained approximate analytical solution of…

Abstract

Purpose

The purpose of this paper is to show how an application of fractional two dimensional differential transformation method (DTM) obtained approximate analytical solution of time‐fraction modified equal width wave (MEW) equation.

Design/methodology/approach

The fractional derivative is described in the Caputo sense.

Findings

It is indicated that the solutions obtained by the two dimensional DTM are reliable and that this is an effective method for strongly nonlinear partial equations.

Originality/value

The paper shows that exact solutions can also be obtained from the known forms of the series solutions.

Article
Publication date: 7 June 2013

Mehmet Merdan, Ahmet Gökdoğan, Ahmet Yildirim and Syed Tauseef Mohyud‐Din

In this article, the aim is to obtain an approximate analytical solution of time‐fraction generalized Hirota‐Satsuma coupled KDV with the help of the two dimensional differential…

Abstract

Purpose

In this article, the aim is to obtain an approximate analytical solution of time‐fraction generalized Hirota‐Satsuma coupled KDV with the help of the two dimensional differential transformation method (DTM). Exact solutions can also be obtained from the known forms of the series solutions.

Design/methodology/approach

Two dimensional differential transformation method (DTM) is used.

Findings

In this paper, the fractional differential transformation method is implemented to the solution of time‐fraction generalized generalized Hirota‐Satsuma coupled KDV with a number of initial and boundary values has been proved. DTM can be applied to many complicated linear and strongly nonlinear partial differential equations and does not require linearization, discretization, restrictive assumptions or perturbation. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial.

Originality/value

This is an original work in which the results indicate that the method is powerful and significant for solving time‐fraction generalized generalized Hirota‐Satsuma coupled KDV type differential equations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 22 March 2013

Behrouz Raftari, Heidar Khosravi and Ahmet Yildirim

The purpose of this paper is to obtain approximate analytical solution of the second order hyperbolic telegraph equation with initial conditions, by the homotopy analysis method…

Abstract

Purpose

The purpose of this paper is to obtain approximate analytical solution of the second order hyperbolic telegraph equation with initial conditions, by the homotopy analysis method (HAM).

Design/methodology/approach

The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions.

Findings

Approximate analytical solution of the second order hyperbolic telegraph equation with initial conditions is obtained by the HAM. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions.

Originality/value

In this work, approximate analytical solution of the second order hyperbolic telegraph equation with initial conditions is obtained by the HAM. To show the efficiency of the present method, several examples are presented.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 19 July 2011

Behrouz Raftari and Ahmet Yildirim

The purpose of this paper is to introduce a new version of the homotopy perturbation method (HPM) for solving the magnetohydrodynamic viscous flow due to a shrinking sheet.

290

Abstract

Purpose

The purpose of this paper is to introduce a new version of the homotopy perturbation method (HPM) for solving the magnetohydrodynamic viscous flow due to a shrinking sheet.

Design/methodology/approach

Three terms from HPM solution are used.

Findings

The results show that this method is very effective and simple and can be applied to other nonlinear problems.

Research limitations/implications

Comparison between the HPM and homotopy analysis methods for the studied problem shows a remarkable agreement and reveals that the HPM needs less work.

Practical implications

It is suggested that this method should be called HPM with auxiliary parameters. This paper uses two auxiliary parameters, three or more auxiliary parameters could be used for accuracy consideration.

Originality/value

In this paper, a two‐parameter HPM is applied which is useful for finding an approximate analytical solution of MHD viscous flow due to a shrinking sheet.

Details

Engineering Computations, vol. 28 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 27 May 2014

Alborz Mirzabeigy and Ahmet Yildirim

The nonlinear jerk equation is a third-order nonlinear equation that describes some physical phenomena and in general form is given by: x = J (x, x, x). The purpose of this paper…

Abstract

Purpose

The nonlinear jerk equation is a third-order nonlinear equation that describes some physical phenomena and in general form is given by: x = J (x, x, x). The purpose of this paper is to employ the modified (MDTM) differential transform method (DTM) to obtain approximate periodic solutions of two cases of nonlinear jerk equation.

Design/methodology/approach

The approach is based on MDTM that is developed by combining DTM, Laplace transform and Padé approximant.

Findings

Comparison of results obtained by MDTM with those obtained by numerical solutions indicates the excellent accuracy of solution.

Originality/value

The MDTM is extended to determining approximate periodic solution of third-order nonlinear differential equations.

Details

Engineering Computations, vol. 31 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 29 March 2011

Syed Tauseef Mohyud‐Din, Ahmet Yildirim and Gülseren Demirli

The purpose of this paper is to consider analytical solution of wave system in Rn with coupling controllers by using the homotopy perturbation method (HPM).

216

Abstract

Purpose

The purpose of this paper is to consider analytical solution of wave system in Rn with coupling controllers by using the homotopy perturbation method (HPM).

Design/methodology/approach

HPM is applied to the system of linear partial differential equations, i.e. the system of waves in the two‐dimensional version of system equations (1) and (2). This problem is motivated by an analogous problem in ordinary differential equations for coupled oscillators and has potential application in isolating a vibrating object from the outside disturbances. For example, rubber or rubber‐like materials can be used to either absorb or shield a structure from vibration. As an approximation, these materials can be modeled as distributed springs.

Findings

In this paper, HPM was used to obtain analytical solution of wave system in with coupling controllers. The method provides the solutions in the form of a series with easily computable terms. Unlike other common methods for solving any physical problem, linear or nonlinear, that requires linearization, discretization, perturbation, or unjustified assumptions that may slightly change the physics of the problem, the HPM finds approximate analytical solutions by using the initial conditions only.

Originality/value

The method proposed in this paper is very reliable and efficient and is being used quite extensively for diversified nonlinear problems of a physical nature. The algorithm is being used for the first time on such problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 2
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.

241

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 September 2012

M.A. Abdou and Ahmet Yildirim

The purpose of this paper is to develop a scheme to study numerical solution of time fractional nonlinear evolution equations under initial conditions by reduced differential…

Abstract

Purpose

The purpose of this paper is to develop a scheme to study numerical solution of time fractional nonlinear evolution equations under initial conditions by reduced differential transform method.

Design/methodology/approach

The paper considers two models of special interest in physics with fractional‐time derivative of order, namely, the time fractional mKdV equation and time fractional convection diffusion equation with nonlinear source term.

Findings

The numerical results demonstrate the significant features, efficiency and reliability of the proposed method and the effects of different values are shown graphically.

Originality/value

The paper shows that the results obtained from the fractional analysis appear to be general.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 16 September 2013

Azizeh Jabbari, Hossein Kheiri and Ahmet Yildirim

– The purpose of this paper is to obtain analytic solutions of telegraph equation by the homotopy Padé method.

151

Abstract

Purpose

The purpose of this paper is to obtain analytic solutions of telegraph equation by the homotopy Padé method.

Design/methodology/approach

The authors used Maple Package to calculate the solutions obtained from the homotopy Padé method.

Findings

The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m, m] homotopy Padé technique are often independent of auxiliary parameter h and this technique accelerates the convergence of the related series. Finally, numerical results for some test problems with known solutions are presented and the numerical results are given to show the efficiency of the proposed techniques.

Originality/value

The paper is shown that homotopy Padé technique is a promising tool with accelerated convergence for complicated nonlinear differential equations.

Details

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

Keywords

Article
Publication date: 30 March 2012

Mohammad Madani, Yasir Khan, Mahdi Fathizadeh and Ahmet Yildirim

The purpose of this paper is to report the effect of radiation on flow of a magneto‐micropolar fluid past a continuously moving plate with suction and blowing.

Abstract

Purpose

The purpose of this paper is to report the effect of radiation on flow of a magneto‐micropolar fluid past a continuously moving plate with suction and blowing.

Design/methodology/approach

The governing equations are transformed into dimensionless nonlinear ordinary differential equations by similarity transformation. Analytical technique, namely the homotopy perturbation method (HPM) combining with Padé approximants and finite difference method, are used to solve dimensionless non‐linear ordinary differential equations. The skin friction coefficient and local Nusselt numbers are also calculated. Beside this, the comparison of the analytical solution with numerical solution is illustrated by the graphs for different values of dimensionless pertinent parameters.

Findings

The authors have studied laminar magneto‐micropolar flow in the presence of radiation by using HPM‐Padé and finite difference methods. Results obtained by HPM‐Padé are in excellent agreement with the results of numerical solution.

Originality/value

The HPM‐Padé is used in a direct way without using linearization, discritization or restrictive assumption. The authors have attempted to show the capabilities and wide‐range applications of the HPM‐Padé in comparison with the finite difference solution of magneto‐micropolar flow in the presence of radiation problem.

Details

Engineering Computations, vol. 29 no. 3
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 3 August 2012

M. Madani, Yasir Khan, Gh. Mahmodi, Naeem Faraz, Ahmet Yildirim and B. Nasernejad

The purpose of this paper is to present the problem of three‐dimensional flow of a fluid of constant density forced through the porous bottom of a circular porous slider moving…

Abstract

Purpose

The purpose of this paper is to present the problem of three‐dimensional flow of a fluid of constant density forced through the porous bottom of a circular porous slider moving laterally on a flat plate.

Design/methodology/approach

The transformed nonlinear ordinary differential equations are solved via the homotopy perturbation method (HPM) for small as well as moderately large Reynolds numbers. The convergence of the obtained HPM solution is carefully analyzed. Finally, the validity of results is verified by comparing with numerical methods and existing numerical results.

Findings

Close agreement of the two sets of results is observed, thus demonstrating the accuracy of the HPM approach for the particular problem considered.

Originality/value

Interesting conclusions which can be drawn from this study are that HPM is very effective and simple compared to the existing solution method, able to solve problems without using Padé approximants and can therefore be considered as a clear advantage over the N.M. Bujurke and Phan‐Thien techniques.

Details

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

Keywords

Content available
Article
Publication date: 1 January 2014

A.J. Chamkha

326

Abstract

Details

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

Expert briefing
Publication date: 1 August 2024

Cracks emerged in the ruling People’s Alliance, a coalition between President Recep Tayyip Erdogan’s Justice and Development Party (AKP) and the Nationalist Movement Party (MHP…

Details

DOI: 10.1108/OXAN-DB288689

ISSN: 2633-304X

Keywords

Geographic
Topical
Article
Publication date: 2 November 2010

Ahmet Yıldırım and Alev Kelleci

This paper aims to directly extend the homotopy perturbation method to study the coupled Burgers equations with time‐ and space‐fractional derivatives.

Abstract

Purpose

This paper aims to directly extend the homotopy perturbation method to study the coupled Burgers equations with time‐ and space‐fractional derivatives.

Design/methodology/approach

The realistic numerical solutions were obtained in a form of rapidly convergent series with easily computable components.

Findings

The figures show the effectiveness and good accuracy of the proposed method.

Originality/value

The paper obtains realistic numerical solutions in a form of rapidly convergent series with easily computable components. It shows the effectiveness and good accuracy of the proposed method.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 13 April 2012

Syed Tauseef Mohyud‐Din, Yasir Khan, Naeem Faraz and Ahmet Yıldırım

The purpose of this paper is to apply exp‐function method to construct generalized solitary and periodic solutions of Fitzhugh‐Nagumo equation, which plays a very important role…

193

Abstract

Purpose

The purpose of this paper is to apply exp‐function method to construct generalized solitary and periodic solutions of Fitzhugh‐Nagumo equation, which plays a very important role in mathematical physics and engineering sciences.

Design/methodology/approach

The authors apply exp‐function method to construct generalized solitary and periodic solutions of Fitzhugh‐Nagumo equation.

Findings

Numerical results clearly indicate the reliability and efficiency of the proposed exp‐function method. The suggested algorithm is quite efficient and is practically well suited for use in these problems.

Originality/value

In this paper, the authors applied the exp‐function method to obtain solutions of the Fitzhugh‐Nagumo equation and show that the exp‐function method gives more realistic solutions without disturbing the basic physics of the physical problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 16 October 2009

Ahmet Yıldırım and Yves Cherruault

The purpose of this paper is to introduce an efficient method for solving susceptible‐infected‐removed (SIR) epidemic model. A SIR model that monitors the temporal dynamics of a…

Abstract

Purpose

The purpose of this paper is to introduce an efficient method for solving susceptible‐infected‐removed (SIR) epidemic model. A SIR model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine. The qualitative analysis reveals the vaccination reproductive number for disease control and eradication. It introduces homotopy perturbation method (HPM) to overcome these problems.

Design/methodology/approach

The paper considers HPM to solve differential system which describes SIR epidemic model. The essential idea of this method is to introduce a homotopy parameter, say p, which takes values from 0 to 1. When p=0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p is gradually increased to 1, the system goes through a sequence of deformations, the solution for each of which is close to that at the previous stage of deformation. One of the most remarkable features of the HPM is that usually just few perturbation terms are sufficient for obtaining a reasonably accurate solution.

Findings

HPM is employed to compute an approximation to the solution of the non‐linear system of differential equations governing the problem.

Originality/value

The paper is of value in presenting, via some tables and figures, some numerical experiments which resulted from applying new methods on test problem.

Details

Kybernetes, vol. 38 no. 9
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 3 May 2013

A. Jabbari, H. Kheiri and A. Yildirim

The purpose of this paper is to obtain analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations by the homotopy analysis and the homotopy Padé methods.

Abstract

Purpose

The purpose of this paper is to obtain analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations by the homotopy analysis and the homotopy Padé methods.

Design/methodology/approach

The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series.

Findings

The approximation solutions by [m,m] homotopy Padé technique is often independent of auxiliary parameter ℏ and this technique accelerates the convergence of the related series.

Originality/value

In this paper, analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations are obtained by the homotopy analysis and the homotopy Padé methods. The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m,m] homotopy Padé technique are often independent of auxiliary parameter ℏ and this technique accelerates the convergence of the related series.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 30 March 2010

Ahmet Yıldırım

This paper aims to present a general framework of the homotopy perturbation method (HPM) for analytic treatment of fractional partial differential equations in fluid mechanics…

Abstract

Purpose

This paper aims to present a general framework of the homotopy perturbation method (HPM) for analytic treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense.

Design/methodology/approach

Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation and fractional Klein‐Gordon equation are investigated to show the pertinent features of the technique.

Findings

HPM is a powerful and efficient technique in finding exact and approximate solutions for fractional partial differential equations in fluid mechanics. The implementation of the noise terms, if they exist, is a powerful tool to accelerate the convergence of the solution. The results so obtained reinforce the conclusions made by many researchers that the efficiency of the HPM and related phenomena gives it much wider applicability.

Originality/value

The essential idea of this method is to introduce a homotopy parameter, say p, which takes values from 0 to 1. When p = 0, the system of equations usually reduces to a sufficiently simplied form, which normally admits a rather simple solution. As p is gradually increased to 1, the system goes through a sequence of deformations, the solution for each of which is close to that at the previous stage of deformation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 4 May 2012

Ahmet Yıldırım and Hüseyin Koçak

The purpose of this paper is to implement the variational iteration method and the homotopy perturbation method to give a rational approximation solution of the foam drainage…

Abstract

Purpose

The purpose of this paper is to implement the variational iteration method and the homotopy perturbation method to give a rational approximation solution of the foam drainage equation with time‐ and space‐fractional derivatives.

Design/methodology/approach

The fractional derivatives are described in the Caputo sense. In these schemes, the solution takes the form of a convergent series with easily computable components.

Findings

Numerical examples are given to demonstrate the effectiveness of the present methods.

Originality/value

Results show that the proposed schemes are very effective and convenient for solving linear and nonlinear fractional differential equations with high accuracy.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 16 March 2020

Kemal Yildirim, Aysen Ozkan, Elif Gunes and Ahmet Mestan

The purpose of this study is to determine the effects of window proximity on perceptions of employees in the call center offices.

Abstract

Purpose

The purpose of this study is to determine the effects of window proximity on perceptions of employees in the call center offices.

Design/methodology/approach

A semantic differential scale composed of nine bipolar adjectives, four of which dealt with “planning,” three of “privacy,” while the rest measured “lighting” was applied for evaluation. In total, 92 employees at the TEPE Call Center in the Bilkent District, Ankara, Turkey participated in the research.

Findings

The results showed that window proximity directly affected the call center employees’ perceptions. In addition, a positive approach was even less affected when the location of the workstation was more at the inner part of the workspace. On the contrary, workstations in front of the window were evaluated more positively, presumably because the employees were happy at feeling roomy and by giving them a higher level of privacy, while also minimizing distractions and interruptions. It was also found that call center employees with secondary education responded more positively than higher educated employees.

Research limitations/implications

This study was limited to examining the effects of window proximity in a call center on employees’ perceptions of an open-plan office. The study supports the results of planning, privacy and lighting, as well as the study on physical environmental factors, such as design, ambient and social, which are thought to be realized in the future.

Originality/value

This study presents suggestions that would be useful for increasing the working and solution-focused perceptual performance values in call center environments from the new generation of work areas. They should be appropriate for the psychological and physical needs of employees in twenty-first-century communication environments, especially in spatial environments and for the suitability of the technological equipment used.

Details

Facilities , vol. 38 no. 7/8
Type: Research Article
ISSN: 0263-2772

Keywords

1 – 20 of 45