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13
New modified variational iteration transform method (MVITM) for solving eighthorder boundary value problems in one step
 World Appl. Sci. J
, 2011
"... Abstract: In this paper, we are development the modified variation iteration method for solving nonlinear equation this method used Laplace transformation, the technique solve nonlinear problem without He's polynomial approximation analytical solution of nonlinear equation by the Laplace transf ..."
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Abstract: In this paper, we are development the modified variation iteration method for solving nonlinear equation this method used Laplace transformation, the technique solve nonlinear problem without He's polynomial approximation analytical solution of nonlinear equation by the Laplace transform method, the scheme is tested for some examples,it is shown that the solution obtained by the Variational Iterational Methods (VIM) and special cases of Homotopy Analysis Method, comparison that solution by Numerical solution solving by Mathematica Software, result also show that numerical scheme is very effective. Key words: Variational iteration method • laplace transform method • nonlinear differential equation homotopy analysis method • nonlinear partial differential equation
A New Analytical Approach to Solve ThomasFermi Equation
 World. Appl. Sci
, 2011
"... Abstract: The aim of this paper is to introduce a new approximate method, namely the Modified Laplace Padé Decomposition Method (MLPDM) which is a combination of modified Laplace decomposition and Padé approximation to provide an analytical approximate solution to ThomasFermi equation. This new ite ..."
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Abstract: The aim of this paper is to introduce a new approximate method, namely the Modified Laplace Padé Decomposition Method (MLPDM) which is a combination of modified Laplace decomposition and Padé approximation to provide an analytical approximate solution to ThomasFermi equation. This new iteration approach provides us with a convenient way to approximate solution. A good agreement between the obtained solution and some wellknown results has been demonstrated. The proposed technique can be easily applied to handle other strongly nonlinear problems. Key words: Modified laplace decomposition method • padé approximants • thomasfermi equation • approximate solution
An Efficient Laplace Decomp osition Algorithm for Fourth Order Parabolic Partial Differential Equations with Variable Coefficients
 World Applied Sciences Journal
, 2011
"... Abstract: The purpose of this article is to introduce a new algorithm, namely Laplace Decomposition Algorithm (LDA) for fourth order parabolic partial differential equations with variable coefficients. This equation arises in the transverse vibration problems. The proposed iterative scheme finds the ..."
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Abstract: The purpose of this article is to introduce a new algorithm, namely Laplace Decomposition Algorithm (LDA) for fourth order parabolic partial differential equations with variable coefficients. This equation arises in the transverse vibration problems. The proposed iterative scheme finds the solution without any discretization, linearization and other restrictive assumptions. Some applications are given to verify the reliability and efficiency of the method. This new algorithm provides us with a convenient way to find exact solution with less computation. Key words: Laplace decomposition algorithm • fourth order parabolic partial differential equations • exact solution
An Efficient Numerical Method for Solving Linear and Nonlinear Partial Differential Equations by Combining Homotopy Analysis and Transform Method
"... Abstract: In this article, we propose a reliable combination of Homotopy analysis method (HAM) and Laplace decomposition method (LDM) to solve linear and nonlinear partial differential equations effectively with less computation. The proposed method is called homotopy analysis transform method (HATM ..."
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Abstract: In this article, we propose a reliable combination of Homotopy analysis method (HAM) and Laplace decomposition method (LDM) to solve linear and nonlinear partial differential equations effectively with less computation. The proposed method is called homotopy analysis transform method (HATM). This study represents significant features of HATM and its capability of handling linear and nonlinear partial differential equations. Key words: Homotopy analysis method • laplace decomposition method • linear and nonlinear partial differential equations • homotopy analysis transform method
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"... Application of the Adomian decomposition method and Laplace transform method to solving the convection diffusiondissipation equation ..."
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Application of the Adomian decomposition method and Laplace transform method to solving the convection diffusiondissipation equation
Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method
, 2015
"... Abstract: Here, a new method called Aboodh transform homotopy perturbation method (ATHPM) is used to solve one dimensional fourth order parabolic linear partial differential equations with variable coefficients. The proposed method is a combination of the new integral transform “Aboodh transform ” a ..."
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Abstract: Here, a new method called Aboodh transform homotopy perturbation method (ATHPM) is used to solve one dimensional fourth order parabolic linear partial differential equations with variable coefficients. The proposed method is a combination of the new integral transform “Aboodh transform ” and the homotopy perturbation method. Some cases of one dimensional fourth order parabolic linear partial differential equations are solved to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. We have compared the obtained analytical solution with the available Aboodh decomposition solution and homotopy perturbation method solution which is found to be exactly same. The results obtained reveal that the combination of Aboodh transform and homotopy perturbation method is quite capable, practically well appropriate for use in such problems.
Laplace Adomian Decomposition Method for Solving NewellWhiteheadSegel Equation
, 2013
"... Abstract In this manuscript, the Laplace Adomian decomposition method (LADM) is presented to solve NewellWhiteheadSegel equation. The method can be applied to linear and nonlinear problems. Some examples have been carried out in order to illustrate the efficiency and reliability of the method. Ma ..."
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Abstract In this manuscript, the Laplace Adomian decomposition method (LADM) is presented to solve NewellWhiteheadSegel equation. The method can be applied to linear and nonlinear problems. Some examples have been carried out in order to illustrate the efficiency and reliability of the method. Mathematics Subject Classification: 35G25
Couple of the Variational Iteration Method and FractionalOrder Legendre Functions Method for Fractional Differential Equations
, 2014
"... We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractionalorder Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms ” is construc ..."
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We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractionalorder Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms ” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Blockpulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique.
DOI: 10.5897/IJPS11.963
, 2011
"... An efficient two step Laplace decomposition algorithm for singular Volterra integral equations ..."
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An efficient two step Laplace decomposition algorithm for singular Volterra integral equations
DOI: 10.5829/idosi.wasj.2012.18.11.1522 Modified Laplace Decomposition Method
"... Abstract: In this paper, the Laplace Decomposition Method (LDM) is improved to obtain approximate analytical solutions of linear and nonlinear differential equations and systems. Based on a new Algorithm of calculating Adomian polynomial’s (AP’s), the proposed algorithm is efficient and simple to ap ..."
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Abstract: In this paper, the Laplace Decomposition Method (LDM) is improved to obtain approximate analytical solutions of linear and nonlinear differential equations and systems. Based on a new Algorithm of calculating Adomian polynomial’s (AP’s), the proposed algorithm is efficient and simple to apply. Some illustrative examples are presented and the results show the significant of our technique. Key words: Laplace decomposition algorithm • adomian polynomials • initial value problems • exact solution • error analysis • system of balance laws