Yazar "Mohyud-Din, Syed Tauseef" seçeneğine göre listele

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    Analytical Approach to a Slowly Deforming Channel Flow with Weak Permeability
    (Walter De Gruyter Gmbh, 2010) Mohyud-Din, Syed Tauseef; Yildirim, Ahmet; Sezer, Sefa Anil
    In this paper, we develop the analytical solution of the Navier-Stokes equations for a semi-infinite rectangular channel with porous and uniformly expanding or contracting walls by employing the homotopy perturbation method (HPM). The series solution of the governing problem is obtained. Some examples have been included. The results so obtained are compared with the existing literature and a remarkable improvement leads to an excellent agreement with the numerical results.
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    Analytical Approach to Space- and Time-Fractional Burgers Equations
    (Iop Publishing Ltd, 2010) Yildirim, Ahmet; Mohyud-Din, Syed Tauseef
    A scheme is developed to study numerical solution of the space- and time-fractional Burgers equations under initial conditions by the homotopy analysis method. The fractional derivatives are considered in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed.
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    Analytical solution of wave system in R-n with coupling controllers
    (Emerald Group Publishing Ltd, 2011) Mohyud-Din, Syed Tauseef; Yildirim, Ahmet; Demirli, Gulseren
    Purpose - The purpose of this paper is to consider analytical solution of wave system in R-n 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.
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    Exp-function method for solitary and periodic solutions of Fitzhugh-Nagumo equation
    (Emerald Group Publishing Limited, 2012) Mohyud-Din, Syed Tauseef; Khan, Yasir; Faraz, Naeem; Yildirim, Ahmet
    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.
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    He's homotopy perturbation method for solving the fractional KdV-Burgers-Kuramoto equation
    (Emerald Group Publishing Limited, 2011) Sezer, Sefa Anil; Yildirim, Ahmet; Mohyud-Din, Syed Tauseef
    Purpose - The purpose of this paper is to directly extend the homotopy perturbation method (HPM) that was developed for integer-order differential equation, to derive explicit and numerical solutions of the fractional KdV-Burgers-Kuramoto equation. Design/methodology/approach - The authors used Maple Package to calculate the functions obtained from the HPM. Findings - The fractional derivatives are described in the Caputo sense. HPM performs extremely well in terms of accuracy, efficiently, simplicity, stability and reliability. Originality/value - The paper describes how the HPM has been successfully applied to find the solution of fractional KdV-Burgers-Kuramoto equation.
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    Heat Transfer Analysis on the Magnetohydrodynamic Flow of a Non-Newtonian Fluid in the Presence of Thermal Radiation: An Analytic Solution
    (Walter De Gruyter Gmbh, 2012) Khan, Yasir; Wu, Qingbiao; Faraz, Naeem; Yildirim, Ahmet; Mohyud-Din, Syed Tauseef
    In this paper, a two-dimensional, steady magnetohydrodynamic flow and heat transfer analysis of a non-Newtonian fluid in a channel with a constant wall temperature are considered in the presence of thermal radiation. The steady Navier-Stokes equations are reduced to nonlinear ordinary differential equations by using similarity variables. The homotopy perturbation method is used to solve the nonlinear ordinary differential equations. The effects of the pertinent parameters on the velocity and temperature field are discussed.
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    Homotopy analysis method for fractional partial differential equations
    (Academic Journals, 2011) Mohyud-Din, Syed Tauseef; Yildirim, Ahmet; Usman, Muhammad
    This paper applies the homotopy analysis method (HAM) to obtain analytical solutions of fractional heat- and wave-like equations with variable coefficients. The applications of the homotopy analysis method were extended to derive analytical solutions in the form of a series with easily computed terms for these generalized fractional equation. Some examples are presented to show the efficiency and simplicity of the method.
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    Homotopy analysis method for space- and time-fractional KdV equation
    (Emerald Group Publishing Limited, 2012) Mohyud-Din, Syed Tauseef; Yildirim, Ahmet; Yuluklu, Eda
    Purpose - The purpose of this paper is to present numerical solutions for the space- and time-fractional Korteweg-de Vries (KdV) equation using homotopy analysis method (HAM). The space and time-fractional derivatives are described in the Caputo sense. The paper witnesses the extension of HAM for fractional KdV equations. Design/methodology/approach - This paper presents numerical solutions for the space- and time-fractional KdV equation using HAM. The space and time-fractional derivatives are described in the Caputo sense. Findings - In this paper, the application of homotopy analysis method was extended to obtain explicit and numerical solutions of the time- and space-fractional KdV equation with initial conditions. The homotopy analysis method was clearly a very efficient and powerful technique in finding the solutions of the proposed equations. Originality/value - In this paper, the application of HAM was extended to obtain explicit and numerical solutions of the time- and space-fractional KdV equation with initial conditions. The HAM was clearly very efficient and powerful technique in finding the solutions of the proposed equations. The obtained results demonstrate the reliability of the algorithm and its wider applicability to fractional nonlinear evolution equations. Finally, the recent appearance of nonlinear fractional differential equations as models in some fields such as the thermal diffusion in fractal media makes it necessary to investigate the method of solutions for such equations and the authors hope that this paper is a step in this direction.
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    Homotopy Perturbation Method for One-Dimensional Hyperbolic Equation with Integral Conditions
    (Walter De Gruyter Gmbh, 2010) Mohyud-Din, Syed Tauseef; Yildirim, Ahmet; Kaplan, Yasemin
    In this study, we use the homotopy perturbation method (HPM) to solve an initial-boundary value problem with a non-classic condition for the one-dimensional wave equation. We will deal with a new type of non-local boundary value problems which are the solution of hyperbolic partial differential equations with a non-standard boundary specification. The method is very reliable and effective and provides the solution in terms of rapid convergent series. Several examples are tested to support our study.
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    Ma's Variation of Parameters Method for Fisher's Equations
    (Global Science Press, 2010) Mohyud-Din, Syed Tauseef; Yildirim, Ahmet
    In this paper, we apply Ma's variation of parameters method (VPM) for solving Fisher's equations. The suggested algorithm proved to be very efficient and finds the solution without any discretization, linearization, perturbation or restrictive assumptions. Numerical results reveal the complete reliability of the proposed VPM.
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    Nonlinear Problems: Analytical and Computational Approach with Applications
    (Hindawi Publishing Corporation, 2012) Noor, Khalida Inayat; Noor, Muhammad Aslam; Mohyud-Din, Syed Tauseef; Yildirim, Ahmet; Momani, Shaher M.
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    Numerical Simulation of Fractional Fornberg-Whitham Equation by Differential Transformation Method
    (Hindawi Publishing Corporation, 2012) Merdan, Mehmet; Gokdogan, Ahmet; Yildirim, Ahmet; Mohyud-Din, Syed Tauseef
    An approximate analytical solution of fractional Fornberg-Whitham equation was obtained with the help of the two-dimensional differential transformation method (DTM). It is indicated that the solutions obtained by the two-dimensional DTM are reliable and present an effective method for strongly nonlinear partial equations. Exact solutions can also be obtained from the known forms of the series solutions.
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    Numerical soliton solution of the Kaup-Kupershmidt equation
    (Emerald Group Publishing Ltd, 2011) Mohyud-Din, Syed Tauseef; Yildirim, Ahmet; Sariaydin, Selin
    Purpose - The purpose of this paper is to obtain soliton solution of the Kaup-Kupershmidt (KK) equation with initial condition. The most important feature of this method is to obtain the solution without direct transformation. Design/methodology/approach - In this paper, the homotopy perturbation method (HPM) is used for obtaining soliton solution of the KK equation. The numerical solutions are compared with the known analytical solutions. The results of numerical examples are presented and only a few terms are required to obtain accurate solutions. Results derived from this method are shown graphically. Findings - The authors obtained the one soliton solution for the KK equation by HPM. The numerical results showed that this method is very accurate. The HPM provides a reliable technique that requires less work if compared with the traditional techniques and the method does not also require unjustified assumptions, linearization, discretization or perturbation. The HPM is very easily applied to both differential equations and linear or nonlinear differential systems. Originality/value - The paper describes how the authors obtained one soliton solution for the KK equation by HPM. The numerical results presented show that this method is very accurate.
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    Numerical soliton solutions of improved Boussinesq equation
    (Emerald Group Publishing Ltd, 2011) Mohyud-Din, Syed Tauseef; Yildirim, Ahmet; Sezer, Sefa Anil
    Purpose - The purpose of this paper is to use the homotopy perturbation method (HPM) to obtain numerical soliton solution of the improved Boussinesq equation (IBE). The solutions are calculated in the form of a convergent power series with easily computable components. Design/methodology/approach - The HPM is used to obtain numerical soliton solution of the IBE. The solutions are calculated in the form of a convergent power series with easily computable components. Findings - The errors are obtained by using the approximate solution given by using only two iterations of the HPM. It is evident that the efficiency of this approach can be dramatically enhanced by computing further terms of approximate solution. Originality/value - The numerical results presented in the paper show that only a few terms are sufficient to obtain accurate solutions.
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    Numerical Solution of the Three-Dimensional Helmholtz Equation
    (Iop Publishing Ltd, 2010) Mohyud-Din, Syed Tauseef; Yildirim, Ahmet
    We apply the homotopy analysis method to solve the nonhomogeneous multidimensional partial differential equation model problem. The analytic solutions are calculated in terms of convergent series with easily computable components. The nonhomogeneous problem is quickly solved by observing the self-canceling "noise" terms whose sum vanishes in the limit. Numerical results clearly reveal the complete reliability and efficiency of the proposed algorithm.
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    Poincare-MacMillan Equations of Motion for a Nonlinear Nonholonomic Dynamical System
    (Iop Publishing Ltd, 2012) Hussain, Amjad; Mohyud-Din, Syed Tauseef; Yildirim, Ahmet
    MacMillan's equations are extended to Poincare's formalism, and MacMillan's equations for nonlinear nonholonomic systems are obtained in terms of Poincare parameters. The equivalence of the results obtained here with other forms of equations of motion is demonstrated. An illustrative example of the theory is provided as well.
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    A reliable algorithm for physical problems
    (Academic Journals, 2011) Usman, Muhammad; Yildirim, Ahmet; Mohyud-Din, Syed Tauseef
    This paper gives a detailed and comprehensive study of a reliable algorithm which is called the Modified Decomposition Method (MDM) and is mainly due to Geijji and Jafari to solve linear and nonlinear problems of physical nature. It has been shown that the MDM is very easy to implement and is fully compatible with the nonlinear nature of the physical problems. Moreover, this algorithm is independent of the inbuilt deficiencies of most of the previous techniques. Several examples are given to re-confirm the reliability and efficiency of the algorithm.
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    Solution of time-fractional generalized Hirota-Satsuma coupled KdV equation by generalised differential transformation method
    (Emerald Group Publishing Ltd, 2013) Merdan, Mehmet; Gokdogan, Ahmet; Yildirim, Ahmet; Mohyud-Din, Syed Tauseef
    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.
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    Solution of time-fractional generalized Hirota-Satsuma coupled KdV equation by generalised differential transformation method
    (Emerald Group Publishing Ltd, 2013) Merdan, Mehmet; Gokdogan, Ahmet; Yildirim, Ahmet; Mohyud-Din, Syed Tauseef
    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.
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    Solution to the MHD flow over a non-linear stretching sheet by homotopy perturbation method
    (Science Press, 2011) Raftari, Behrouz; Mohyud-Din, Syed Tauseef; Yildirim, Ahmet
    In this study, by means of homotopy perturbation method (HPM) an approximate solution of the magnetohydrodynamic (MHD) boundary layer flow is obtained. The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve. HPM produces analytical expressions for the solution to nonlinear differential equations. The obtained analytic solution is in the form of an infinite power series. In this work, the analytical solution obtained by using only two terms from HPM solution. Comparisons with the exact solution and the solution obtained by the Pade approximants and shooting method show the high accuracy, simplicity and efficiency of this method.