In mathematics and physics, perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. Ismail, â, Somjate Duangpithak and Montri Torvattanabun, â. The proposed method introduces also He’s polynomials [1]. Recently, the generalized homotopy method (GHM) [1] was proposed as a generalization of the homotopy perturbation method (HPM). 6(2), p- 163-168, 2005. Copyright © 2019 Scientific & Academic Publishing Co. All rights reserved. 2009; 58 (11–12):2134–2141. Many mathematical Nonlinear phenomena have important applications in applied mathematics, physics, and issues related to engineering. Examples of one-dimensional and two-dimensional are presented to show the ability of the method for such equations. Copyright © 2007 Elsevier B.V. All rights reserved. The proposed iterative scheme ﬁnds the solu- A Study On Linear and Non linear Schrodinger Equations by Reduced Differential Transform Method. A graphical representation of the result has been shown which provides the most accurate physical situation and accuracy of the solution. American Journal of Mathematics and Statistics, 2019; B. Md. The application of such method is based on a power series matching that enables GHM to obtain complex and rich expression impossible to obtain using HPM. The aim of this Letter is to present an efficient and reliable treatment of the homotopy perturbation method (HPM) for nonlinear partial differential equations with fractional time derivative. This work presents the homotopy perturbation transform method for nonlinear fractional partial differential equations of the Caputo-Fabrizio fractional operator. M. El- Shahed, Moustafa, âApplication of Heâs Homotopy Perturvation Method to Volterraâs Integro- differential Equation, International Journal of Nonlinear Science of Simulationâ, Vol. The HPTM is a hybrid of Laplace transform and homotopy perturbation method. equations, system of ordinary and partial differential equations and integral equations. Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method. From the calculation and its graphical representation it is clear that how the solution of the equation and its behavior depends on the initial conditions. The obtained results are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, efficient and easy to implement. In this paper a new method called Elzaki transform homotopy perturbation method (ETHPM) is described to obtain the exact solution of nonlinear systems of partial differential equations. Homotopy perturbation method (HPM) is a semi‐analytical technique for solving linear as well as nonlinear ordinary/partial differential equations. Sweilam NH, Khader MM. This article confirms the power, simplicity and efficiency of the method compared with the exact solution. The fractional derivative is described in the Caputo sense. Perturbative expansion polynomials are considered to obtain an infinite series solution. The results reveal that the method is very effective and simple. The HPM allows to find the solution of the nonlinear partial differential equations which will be calculated in the form of a series with easily computable components. Keywords: This method was found to be more efficient and easy to solve linear and nonlinear differential equations. Copyright Â© 2019 The Author(s). T.R. The algorithm is tested for a single equation, coupled two equations, and coupled three equations. This … We apply a relatively new technique which is called the homotopy perturbation method (HPM) for solving linear and nonlinear partial differential equations. Perturbation iteration method has been recently constructed and it has been also proven that this technique is very effective for solving some nonlinear differential equations. Key-Words Homotopy Perturbation Method- Drinfeld-Sokolov equation- Modiﬁed Benjamin Bona-Mahony equa-tion 1 Introduction The Drinfeld-Sokolov (DS) system was ﬁrst intro-duced by Drinfeld and Sokolov and it is a system of nonlinear partial differential equations owner of the In this paper, the homotopy perturbation method (HPM) is extended to obtain analytical solutions for some nonlinear differential-difference equations (NDDEs). Homotopy perturbation method is simply applicable to the different non-linear partial differential equations. Solving nonlinear differential equations is an important task in sciences because many physical phenomena are modelled using such equations. The effectiveness of this method is demonstrated by finding the exact solutions of the fractional equations proposed, for the special case … Chaos, Solitons and Fractals, 26:(2005),695-700. An elegant and powerful technique is Homotopy Perturbation Method (HPM) to solve linearand nonlinear partial differential equations. One method I know is by splitting the equation to linear and nonlinear parts such that the nonlinear part is "small" is some sense and then treating it as a perturbation. Application of homotopy perturbation method to nonlinear wave equations. [2] J. H. He. In this paper, the homotopy perturbation method (HPM) is extended to obtain analytical solutions for some nonlinear differential-difference equations (NDDEs). The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. The homotopy–perturbation method is applied to bifurcation of nonlinear problems by He and to integro-differential system by El-Shahed . Homotopy perturbation method, Approximate solution, Exact solution, Nonlinear Reaction-Diffusion-Convection problem. We extend He's homotopy perturbation method (HPM) with a computerized symbolic computation to find approximate and exact solutions for nonlinear differential difference equations (DDEs) arising in physics. The method may also be used to solve a system of coupled linear and nonlinear differential equations. Sparked by demands inherent to the mathematical study of pollution, intensive industry, global warming, and the biosphere, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems is the first book ever to systematically present the theory of adjoint equations for nonlinear problems, as well as their application to perturbation algorithms. One of the most powerful methods to approximately solve nonlinear differential equations is the homotopy perturbation method (HPM) (Aminikhah 2012; Barari et al. "The present textbook shows how to find approximate solutions to nonlinear differential equations (both ordinary and partial) by means of asymptotic expansions. Comput Math Appl. In this paper, Drinfeld-Sokolov and Modified Benjamin-Bona-Mahony equations are is studied perturbatively by using homotopy perturbation method. Despite the importance of obtaining the exact solution of nonlinear partial differential equations in physics and applied mathematics, there is still the daunting problem of finding new … An elegant and powerful technique is Homotopy Perturbation Method (HPM) to solve linearand nonlinear partial differential equations. Using the initial conditions this method provides an analytical or exact solutions. Elzaki transform is a powerful tool for solving some differential equations which can not solve by Sumudu transform in [(2012)]. In this article, we shall be applied this method to get most accurate solution of a highly non-linear partial differential equation which is Reaction-Diffusion-Convection Problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. Result and Discussion of the Solution of Equation (10). as homotopy perturbation method [1-5], Adomian's transform is defined as follows, Elzaki transform of the decomposition method [6], differential transform method functionf(t) is [6-11] and projected differential transform method [8, 12] to solve linear and nonlinear differential equations. [3] J. H. He. Using the initial conditions this method provides an analytical or exact solutions. In this paper, homotopy perturbation method is applied to solve non -linear Fredholm integro differential equations of … On leave from Department of Mathematics, Mutah University, Jordan. This work is licensed under the Creative Commons Attribution International License (CC BY). 3, 2019, pp. Most of the methods have been utilized in linear problems and a few numbers of works have considered nonlinear problems. The aim of this paper is to present He’s Homotopy Perturbation Method (HPM) with Modification (MHPM) which are the semi-analytical technique and applying it to solve the Fredholm-Hammerstein type of multi-higher order nonlinear integro-fractional differential equations with variable coefficients and under given mixed conditions. The fractional derivative is described in the Caputo sense. tively by using homotopy perturbation method. Ramesh Chand Mittal and Rakesh Kumar Jan. Ramesh Rao a,∗ a Department of Mathematics and Actuarial Science, B.S. The discretized modified Kortewegde Vries (mKdV) lattice equation and the discretized nonlinear Schrodinger equation are taken as examples to illustrate the validity and the great potential of the HPM in solving such NDDEs. The iteration algorithm for systems is developed first. Key words:Homotopy perturbation method; Nonlinear integro-differential equations; Fractional differential equations INTRODUCTION Mathematical modeling of real-life problem usually results in functional equations, e.g. Cite this paper: M. Tahmina Akter, M. A. Mansur Chowdhury, Homotopy Perturbation Method for Solving Highly Nonlinear Reaction-Diffusion-Convection Problem, American Journal of Mathematics and Statistics, Vol. The suggested method is adopted by Cveticanin [30] for solving differential equations with complex functions. The analytical results of examples are calculated in terms of convergent series with easily computed components [2]. Homotopy perturbation method; Special nonlinear partial differential equations Abstract In this article, homotopy perturbation method is applied to solve nonlinear parabolic– hyperbolic partial differential equations. http://creativecommons.org/licenses/by/4.0/. The suggested algorithm is quite efﬁcient and is practically well suited for use in these problems. Book Description. The homotopy perturbation method for nonlinear oscillators with discontinuities.Applied Mathematics and Computation, 151:(2004),287-292. A modified homotopy perturbation method coupled with the Fourier transform for nonlinear and singular Lane–Emden equations A. Nazari-Golshan, S.S. Nourazar, H. Ghafoori-Fard, A. Yildirim and A. Campo By continuing you agree to the use of cookies. This paper deals the implementation of homotopy perturbation transform method (HPTM) for numerical computation of initial valued autonomous system of time-fractional partial differential equations (TFPDEs) with proportional delay, including generalized Burgers equations with proportional delay. The proposed method was derived by combining Elzaki transform and homotopy perturbation method. In this paper, we present a new method, a mixture of homotopy perturbation method and a new integral transform to solve some nonlinear partial differential equations. Published by Scientific & Academic Publishing. In this paper, we combined Elzaki transform and homotopy perturbation to solve nonlinear partial differential equations. doi: 10.1016/j.camwa.2009.03.059. partial differential equations, integral and integro-differential equations, stochastic equations and others. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. Homotopy perturbation method for nonlinear partial differential equations of fractional order. Correspondence to: M. Tahmina Akter, Department of Mathematics, Chittagong University of Engineering & Technology, Chittagong, Bangladesh. The aim of this Letter is to present an efficient and reliable treatment of the homotopy perturbation method (HPM) for nonlinear partial differential equations with fractional time derivative. http://creativecommons.org/licenses/by/4.0/, 4. In this study, we develop the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. The previously developed new perturbation-iteration algorithm has been applied to differential equation systems for the first time. The discretized modified Kortewegde Vries (mKdV) lattice equation and the discretized nonlinear Schrodinger equation are taken as examples to illustrate the validity and the great potential of the HPM in solving such NDDEs. 136-141. doi: 10.5923/j.ajms.20190903.04. We use cookies to help provide and enhance our service and tailor content and ads. Abdur Rahman University, Chennai-600 048, TamilNadu, India.. Abstract. method [2] and differential transform method [1]. This article also confirmed that this method is suitable method for solving any types of partial differential equations. 9 No. Therefore, using as a guide the main idea of power series matching, be… Nonlinear equations are of great importance to our contemporary world. Homotopy Perturbation Method for Nonlinear Ill-posed Operator Equations Homotopy Perturbation Method for Nonlinear Ill-posed Operator Equations Cao , , Li; Han , , Bo; Wang , , Wei 2009-10-01 00:00:00 This paper suggests a new iteration algorithm for solving nonlinear ill-posed equations by the homotopy perturbation method. Copyright © 2020 Elsevier B.V. or its licensors or contributors. In this article, we shall be applied this method to get most accurate solution of a highly non-linear partial differential equation which is Reaction-Diffusion-Convection Problem. Two numerical tests with nonlinear ill-posed operators are given. Graphical Representation of above Equation, 5. There are several analytical methods, such as homotopy analysis method (HAM) , homotopy perturbation method (HPM) , Adomian decomposition method (ADM) , variational iteration method (VIM) , and a new iterative method , are available to solve nonlinear fractional partial differential equations. https://doi.org/10.1016/j.physleta.2007.01.046. 9(3): 136-141, M. Tahmina Akter1, M. A. Mansur Chowdhury2, 1Department of Mathematics, Chittagong University of Engineering & Technology, Chittagong, Bangladesh, 2Jamal Nazrul Islam Research Center for Mathematical and Physical Sciences (JNIRCMPS), University of Chittagong, Chittagong, Bangladesh.

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