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185
Variational approach for nonlinear oscillators
 Chaos, Solitons and Fractals 34:1430–1439
, 2007
"... This paper suggests a novel method called maxmin method. Maximal and minimal solution thresholds of a nonlinear problem can be easily found, and an approximate solution of the nonlinear equation can be easily deduced using He Chengtian’s interpolation, which has millennia history. Application of th ..."
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Cited by 26 (0 self)
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This paper suggests a novel method called maxmin method. Maximal and minimal solution thresholds of a nonlinear problem can be easily found, and an approximate solution of the nonlinear equation can be easily deduced using He Chengtian’s interpolation, which has millennia history. Application of the method to nonlinear oscillators is systematically illustrated, illustrating examples show the present technology is very convenient and effective.
Modified variational iteration methods for ThomasFermi equation
 Wd. Appl. Sci. J
, 2008
"... Abstract: In this paper, we implement and compare two modified versions of variational iteration method (VIM) for obtaining the approximate solution of ThomasFermi (TF) equation which plays a very important role in applied sciences. These modifications are made by introducing He’s and Adomian’s po ..."
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Cited by 10 (3 self)
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Abstract: In this paper, we implement and compare two modified versions of variational iteration method (VIM) for obtaining the approximate solution of ThomasFermi (TF) equation which plays a very important role in applied sciences. These modifications are made by introducing He’s and Adomian’s polynomials in the correction functional of the VIM. The analytical results are calculated in terms of convergent series with easily computable components. The initial slope of the ThomasFermi potential y′(0) is computed by converting the obtained series solution into several diagonal Pade ´ approximants. Numerical results reveal the complete reliability of the proposed iterative schemes. Moreover, it is observed that modification based on He’s polynomials; though compatible with the one obtained by employing Adomian’s polynomials is yet much simpler and is easier to implement.
Applications of Homotopy Perturbation Transform Method for Solving TimeDependent Functional Differential Equations.
 Int. J. Nonlinear Sci,
, 2013
"... Abstract: In this paper, we apply homotopy perturbation transform method for solving linear and nonlinear functional differential equations. This method is a combined form of the Laplace transform method with the homotopy perturbation method. The nonlinear terms can be easily handled by the use of ..."
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Cited by 8 (2 self)
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Abstract: In this paper, we apply homotopy perturbation transform method for solving linear and nonlinear functional differential equations. This method is a combined form of the Laplace transform method with the homotopy perturbation method. The nonlinear terms can be easily handled by the use of He's polynomials. This technique finds the solutions without any discretization or restrictive assumptions and free from roundoff errors and therefore reduces the numerical computations to a great extent. The results are also given to demonstrate the validity and applicability of the present technique. Also the results reveal that the homotopy perturbation transform method is very efficient, simple and can be applied to other nonlinear problems. The fact that this technique solves nonlinear problems without using Adomain's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.
Effects of a crack on the stability of a nonlinear rotor system
 International Journal of NonLinear Mechanics
, 2007
"... The stability of a rotor system presenting a transverse breathing crack is studied by considering the effects of crack depth, crack location and the shaft’s rotational speed. The harmonic balance method, in combination with a pathfollowing continuation procedure, is used to calculate the periodic r ..."
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Cited by 7 (0 self)
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The stability of a rotor system presenting a transverse breathing crack is studied by considering the effects of crack depth, crack location and the shaft’s rotational speed. The harmonic balance method, in combination with a pathfollowing continuation procedure, is used to calculate the periodic response of a nonlinear model of a cracked rotor system. The stability of the rotor’s periodic movements is studied in the frequency domain by introducing the effects of a perturbation on the periodic solution for the cracked rotor system. It is shown that the areas of instability increase considerably when the crack deepens, and that the crack’s position and depth are the main factors affecting not only the nonlinear behaviour of the rotor system but also the different zones of dynamic instability in the periodic solution for the cracked rotor. The effects of some other system parameters (including the disk position and the stiffness of the supports) on the dynamic stability of the nonlinear periodic response of the cracked rotor system are also investigated.
A local fractional variational iteration method for Laplace equation within local fractional operators,”
 Abstract and Applied Analysis,
, 2013
"... The local fractional variational iteration method for local fractional Laplace equation is investigated in this paper. The operators are described in the sense of local fractional operators. The obtained results reveal that the method is very effective. ..."
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Cited by 5 (3 self)
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The local fractional variational iteration method for local fractional Laplace equation is investigated in this paper. The operators are described in the sense of local fractional operators. The obtained results reveal that the method is very effective.
Numerical solutions of the nonlinear integrodifferential equations
 Int. J. Open Problems Compt. Math
, 2008
"... This paper compares the variational iteration method (VIM) with the Adomian decomposition method (ADM) for solving nonlinear integro differential equations. From the computational viewpoint, the VIM is more efficient, convenient and easy to use. ..."
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Cited by 4 (0 self)
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This paper compares the variational iteration method (VIM) with the Adomian decomposition method (ADM) for solving nonlinear integro differential equations. From the computational viewpoint, the VIM is more efficient, convenient and easy to use.
Approximate Solutions of Twelfthorder Boundary Value Problems SYED TAUSEEF MOHYUDDIN,
"... In this paper, we implement a relatively new analytical technique which is called the variational iteration method for solving the twelfthorder boundary value problems by converting the problems into a system of integral equations. The analytical results of the problems have been obtained in terms ..."
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Cited by 4 (4 self)
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In this paper, we implement a relatively new analytical technique which is called the variational iteration method for solving the twelfthorder boundary value problems by converting the problems into a system of integral equations. The analytical results of the problems 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 suggested technique. The fact that variational iteration method solves nonlinear problems without using the Adomian’s polynomials is a clear advantage of this technique over the decomposition method.
Homotopy analysis method for solving KDV equations
 Surveys in Math. Appl
"... Abstract. A scheme is developed for the numerical study of the Kortewegde Vries (KdV) and the Kortewegde Vries Burgers (KdVB) equations with initial conditions by a homotopy approach. Numerical solutions obtained by homotopy analysis method are compared with exact solution. The comparison shows t ..."
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Abstract. A scheme is developed for the numerical study of the Kortewegde Vries (KdV) and the Kortewegde Vries Burgers (KdVB) equations with initial conditions by a homotopy approach. Numerical solutions obtained by homotopy analysis method are compared with exact solution. The comparison shows that the obtained solutions are in excellent agreement.
Numerical Solutions of the Linear Volterra Integrodifferential Equations: Homotopy Perturbation Method and Finite Difference Method
"... Abstract: In the research, special type of linear volterra integrodifferential equations is considered. This paper compares the Homotopy perturbation method (HPM) with finite difference method for solving these equations. HPM is an analytical procedure for finding the solutions of problems which is ..."
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Abstract: In the research, special type of linear volterra integrodifferential equations is considered. This paper compares the Homotopy perturbation method (HPM) with finite difference method for solving these equations. HPM is an analytical procedure for finding the solutions of problems which is based on the constructing a Homotopy with an imbedding parameter p that is considered as a small parameter. The finite difference method, based upon Simpson rule and Trapezoidal rule, transforms the volterra integrodifferential equation into a matrix equation. The results of applying these methods to the linear integrodifferential equation show the simplicity and efficiency of these methods. Key words: Volterra integrodifferential equations • homotopy perturbation method • finite difference method
Variational Iteration Method for Solving Initial and Boundary Value Problems of Bratutype
, 2007
"... In this paper, we present a reliable framework to solve the initial and boundary value problems of Bratutype which are widely applicable in fuel ignition of the combustion theory and heat transfer. The algorithm rests mainly on a relatively new technique, the variational iteration method. Several e ..."
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Cited by 3 (0 self)
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In this paper, we present a reliable framework to solve the initial and boundary value problems of Bratutype which are widely applicable in fuel ignition of the combustion theory and heat transfer. The algorithm rests mainly on a relatively new technique, the variational iteration method. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm.