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Solving Higher-Order Integro-Differential Equations Using He`s Polynomials
Syed Tauseef Mohyud Din,Muhammad Aslam Noor 한국산업응용수학회(구 한국산업정보응용수학회) 2009 한국산업정보응용수학회 Vol.13 No.2
In this paper, we use He`s polynomials for solving higher order integro differential equations (IDES) by converting them to an equivalent system of integral equations. The He`s polynomials which are easier to calculate and are compatible to Adomian`s polynomials are found by using homotopy perturbation method. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Several examples are given to verify the reliability and efficiency of the proposed method.
SOLVING HIGHER-ORDER INTEGRO-DIFFERENTIAL EQUATIONS USING HE'S POLYNOMIALS
SYED TAUSEEF MOHYUD-DIN,MUHAMMAD ASLAM NOOR 한국산업응용수학회 2009 Journal of the Korean Society for Industrial and A Vol.13 No.2
In this paper, we use He's polynomials for solving higher order integro differential equations (IDES) by converting them to an equivalent system of integral equations. The He's polynomials which are easier to calculate and are compatible to Adomian's polynomials are found by using homotopy perturbation method. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Several examples are given to verify the reliability and efficiency of the proposed method.
Syed Tauseef Mohyud-Din,Ahmet Yildirim 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.1
The aim of the paper is to apply Homotopy Perturbation Method (HPM) for the solution of a nonlinear fractional differential equation. Finally, the solution obtained by the Homotopy perturbation method has been numerically evaluated and presented in the form of tables and then compared with those obtained by truncated series method. A good agreement of the results is observed.
SOLUTION OF TENTH AND NINTH-ORDER BOUNDARY VALUE PROBLEMS BY HOMOTOPY PERTURBATION METHOD
SYED TAUSEEF MOHYUD-DIN,AHMET YILDIRIM 한국산업응용수학회 2010 Journal of the Korean Society for Industrial and A Vol.14 No.1
In this paper, we apply homotopy perturbation method (HPM) for solving ninth and tenth-order boundary value problems. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed homotopy perturbation method solves nonlinear problems without using Adomian’s polynomials can be considered as a clear advantage of this technique over the decomposition method.
Mohyud-Din, Syed Tauseef,Yildirim, Ahmet The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.1
The aim of the paper is to apply Homotopy Perturbation Method (HPM) for the solution of a nonlinear fractional differential equation. Finally, the solution obtained by the Homotopy perturbation method has been numerically evaluated and presented in the form of tables and then compared with those obtained by truncated series method. A good agreement of the results is observed.
VARIATION OF PARAMETERS METHOD FOR SOLVING SIXTH-ORDER BOUNDARY VALUE PROBLEMS
Mohyud-Din, Syed Tauseef,Noor, Muhammad Aslam,Waheed, Asif Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.4
In this paper, we develop a reliable algorithm which is called the variation of parameters method for solving sixth-order boundary value problems. The proposed technique is quite efficient and is practically well suited for use in these problems. The suggested iterative scheme finds the solution without any perturbation, discritization, linearization or restrictive assumptions. Moreover, the method is free from the identification of Lagrange multipliers. The fact that the proposed technique solves nonlinear problems without using the Adomian's polynomials can be considered as a clear advantage of this technique over the decomposition method. Several examples are given to verify the reliability and efficiency of the proposed method. Comparisons are made to reconfirm the efficiency and accuracy of the suggested technique.
VARIATIONAL DECOMPOSITION METHOD FOR SOLVING SIXTH-ORDER BOUNDARY VALUE PROBLEMS
Noor, Muhammad Aslam,Mohyud-Din, Syed Tauseef The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper, we implement a relatively new analytical technique by combining the traditional variational iteration method and the decomposition method which is called as the variational decomposition method (VDM) for solving the sixth-order boundary value problems. The proposed technique is in fact the modification of variatioanal iteration method by coupling it with the so-called Adomian's polynomials. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Comparisons are made to verify the reliability and accuracy of the proposed algorithm. Several examples are given to check the efficiency of the proposed algorithm. We have also considered an example where the VDM is not reliable.
Variational decomposition method for solving sixth-order boundary value problems
Muhammad A. Noor,Syed Tauseef Mohyud-Din 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper, we implement a relatively new analytical technique by combining the traditional variational iteration method and the decomposition method which is called as the variational decomposition method (VDM) for solving the sixth-order boundary value problems. The proposed technique is in fact the modification of variatioanal iteration method by coupling it with the so-called Adomian's polynomials. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Comparisons are made to verify the reliability and accuracy of the proposed algorithm. Several examples are given to check the efficiency of the proposed algorithm. We have also considered an example where the VDM is not reliable. In this paper, we implement a relatively new analytical technique by combining the traditional variational iteration method and the decomposition method which is called as the variational decomposition method (VDM) for solving the sixth-order boundary value problems. The proposed technique is in fact the modification of variatioanal iteration method by coupling it with the so-called Adomian's polynomials. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Comparisons are made to verify the reliability and accuracy of the proposed algorithm. Several examples are given to check the efficiency of the proposed algorithm. We have also considered an example where the VDM is not reliable.
Squeezing Flow of Micropolar Nanofluid between Parallel Disks
Sheikh Irfanullah Khan,Syed Tauseef Mohyud-Din,Yang Xiao-Jun 한국자기학회 2016 Journal of Magnetics Vol.21 No.3
In the present study, squeezing flow of micropolar nanofluid between parallel infinite disks in the presence of magnetic field perpendicular to plane of the disks is taken into account. The constitutive equations that govern the flow configuration are converted into nonlinear ordinary differential with the help of suitable similarity transforms. HAM package BVPh2.0 has been employed to solve the nonlinear system of ordinary differential equations. Effects of different emerging parameters like micropolar parameter K, squeezed Reynolds number R, Hartmann number M, Brownian motion parameter Nb, thermophoresis parameter Nt, Lewis number Le for dimensionless velocities, temperature distribution and concentration profile are also discussed graphically. In the presence of strong and weak interaction (i.e. n = 0 and n = 0.5), numerical values of skin friction coefficient, wall stress coefficient, local Nusselt number and local Sherwood number are presented in tabulated form. To check the validity and reliability of the developed algorithm BVPh2.0 a numerical investigation is also a part of this study.
M. Aslam Noor,Khalida Inayat Noor,Syed Tauseef Mohyud-Din,Noor Ahmed Shaikh 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods. In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods.