Basic idea of homotopy perturbation method to illustrate the basic ideas of the new method, we consider the following nonlinear differential equation 1 au. The application of the homotopy analysis method and the homotopy perturbation method to the daveystewartson equations and comparison between them and exact solutions zedan, hassan a. Assessment of hes homotopy perturbation method for optimal. In this paper, we apply a new method called elzaki transform homotopy perturbation method ethpm to solve porous medium equation. This numerical method is applied on a previously available case study.
Dec 06, 2016 khalid suliman aboodh, solving fourth order parabolic pde with variable coefficients using aboodh transform homotopy perturbation method, pure and applied mathematics journal 2015. Nonlinearities distribution laplace transformhomotopy perturbation. The homotopy perturbation method hpm has been used to investigate a variety of mathematical and physical problems, since it is very. The combination of the perturbation method and the homotopy method is called the homotopy perturbation method hpm, which has eliminated limitations of the traditional perturbation techniques. Homotopy perturbation method for linear programming. In our previous work, homotopy perturbation method has been used to evaluate thermal performance of. Assessment of hes homotopy perturbation method 353 while p varies in the span of 0, 1, the solution of linear parts of x. Assessment of hes homotopy perturbation method for. Homotopy perturbation method and elzaki transform for. The application of the homotopy analysis method and the. Nonlinearities distribution laplace transformhomotopy.
In the research, special type of linear volterra integrodifferential equations is considered. The homotopy perturbation method introduced by the chinese researcher dr. The homotopy perturbation method hpm and the decomposition of a source function are used together to develop this new technique. A detailed illustration on choosing linear operators is given in 12.
M modified homotopy perturbation method coupled with laplace transform 1410 thermal science, year 20, vol. Homotopy perturbation method the essence of the homotopy perturbation method is the introduction of the homotopy parameter p which takes the value from 0 to 1. Application of homotopy perturbation transform method to. Moreover, solving of convectiondiffusion equations has been developed by hpm and the convergence properties of the proposed method have been analyzed in detail. In this paper, we employ a new homotopy perturbation method to obtain the solution of a firstorder inhomogeneous pde. On the application of homotopy perturbation method for. The nonlinear term can be easily handled by homotopy perturbation method.
Hypersingular integral equations of the first kind. Use of homotopy perturbation method for solving multipoint. Homotopy perturbation method for solving systems of nonlinear coupled equations a. We introduce two powerful methods to solve the daveystewartson equations. While h,s are nonlinear functions and k, mp, are integers. Pdf analysis of the new homotopy perturbation method for linear. Rabbani and others published new homotopy perturbation method to solve nonlinear problems find, read and cite all the. Research article a new spectralhomotopy perturbation. Pdf in this article, a new homotopy technique is presented for the mathematical analysis of finding. Analytical approach for nonlinear partial analytical.
In this method, according to the homotopy technique, a homotopy with an imbedding parameter p. In this method, each decomposition of the source function f x, y leads to a new homotopy. An analytic method for strongly nonlinear problems, namely the homotopy analysis method ham was proposed by liao in 1992, six years earlier than the homotopy perturbation method by he h. Application of hes homotopy perturbation method int. Hilal 2012, homotopy perturbation and elzaki transform for solving nonlinear partial differential equations. Modified homotopy perturbation method for nonlinear system of. Homotopy perturbation method for solving systems of nonlinear. Different from perturbation techniques, the ham is valid if a nonlinear problem.
View homotopy perturbation method research papers on academia. In section 3, we point out the problems of the mentioned paper. The basic concept of general homotopy perturbation method is given in appendix a. Homotopy perturbation method and elzaki transform for solving. Variational homotopy perturbation method for solving. An application of homotopy perturbation method for non. By the homotopy technique in topology, a homotopy is constructed with an imbedding parameter p. In this paper, a new technique has been used forsolving the porous medium equation.
Biazar and ghazvini 31, in turn, applied the homotopy perturbation method for solving the hyperbolic partial differential equation. Analysis of the new homotopy perturbation method for. The aboodh transformbased homotopy perturbation method athpm is applied to get the approximate analytical solution for the generalized equation and hence some physically relevant anharmonic oscillators are studied as the special cases of this solution. Research article modified homotopy perturbation method for. Homotopy perturbation method for solving systems of. Sep 22, 20 in the present paper, we study a homogeneous cosmological model in friedmannrobertsonwalker frw spacetime by means of the socalled homotopy perturbation method hpm. He 38 developed the homotopy perturbation method for solving linear, nonlinear, ini. Variational homotopy perturbation method for solving riccati.
The results reveal that the proposed method is very effective and simple. First, we briefly recall the main equations of the cosmological model and the basic idea of hpm. The boundary conditions of problem are considered with both sides simply supported and simply supportedclamped. Panda 20, some recently developed analytical methods namely. Analysis of the new homotopy perturbation method for linear and. The homotopy perturbation method hpm and the decomposition of a. In this study, the homotopy perturbation method hpm is applied for free vibration analysis of beam on elastic foundation. Study of strongly nonlinear oscillators using the aboodh. Perturbative expansion polynomials are considered to obtain an infinite series solution. This method was found to be more efficient and easy to solve linear and nonlinear differential equations. He he, 1999, 2003, 2004, 2005 developed the homotopy perturbation method for solving. New improved variational homotopy perturbation method for. A comparison between the differential transform method and homotopy perturbation method for a system of non linear chemistry problems. Application of the homotopy perturbation method to coupled system of partial differential.
This method is a combination of the new integral transform elzaki transform and the homoto py perturbation method. Homotopy perturbation method for temperature distribution. In this article, we shall be applied this method to get most accurate solution of a highly nonlinear partial differential equation which is reactiondiffusionconvection problem. Comparison of the hpm results with the ham results, and compute the absolute errors between the exact solutions of the ds equations with the hpm. Analysis of nonlinear reactiondiffusion processes with. Ham is a strong and easy to use analytic tool for nonlinear problems. The aboodh transformbased homotopy perturbation method athpm is applied to get the approximate analytical solution for the generalized equation and hence some physically relevant anharmonic oscillators are studied as the special cases. In order to illustrate the potentiality of the approach. On the other hand, this technique can have full advantage of the traditional perturbation techniques. An elegant and powerful technique is homotopy perturbation method hpm to solve linearand nonlinear partial differential equations. Nonlinear vibration analysis of functionally graded. Next we consider the test example when the exact solution of the model is known, in order to approbate the. Homotopy perturbation method hpm for linear systems. Homotopy perturbation method for solving partial differential.
Convergence analysis of homotopy perturbation method for volterra integrodifferential equations of fractional order. When,p 0 the equation or system of equations takes a simplified form whose solution can be readily obtained analytically. A modified homotopy perturbation method and its application to vibration and active control. In this article, we focus on linear and nonlinear fuzzy volterra integral equations of the second kind and we propose a numerical scheme using homotopy perturbation method hpm to obtain fuzzy approximate solutions to them. In this paper, a variational homotopy perturbation method is proposed to solve nonlinear riccati differential equation. The proposed method was derived by combining elzaki transform and homotopy perturbation method. Homotopy perturbation transform method for nonlinear. Research article a new spectralhomotopy perturbation method. Journal of low frequency noise, vibration and active control, vol. Using the initial conditions this method provides an analytical or exact solutions.
Homotopy perturbation method for solving some initial. Cheniguel is with department of mathematics and computer science. Numerical solutions of the linear volterra integro. The effectiveness of this method is demonstrated by finding the exact solutions of the fractional equations proposed, for the special case. Modified homotopy perturbation method for nonlinear system.
In our previous work, homotopy perturbation method has been used to evaluate thermal performance of straight fins with constant thermal conductivity. Journal of applied mathematics and statistics, 2, 231234. He, a coupling method of a homotopy technique and a perturbation technique for nonlinear problems, internat. Introduction the homotopy perturbation method hpm was established by jihuan he in 1999 23. The method is a simple modification of the standard homotopy perturbation method hpm, in which it is treated as an algorithm in a sequence of small intervals i. Hemeda department of mathematics, faculty of science, tanta university, tanta, egypt.
Use of homotopy perturbation method for solving multi. Using new homotopy perturbation me thod 24, the approximate analytical solution of eq. Analytical approach for nonlinear partial analytical approach. Application of homotopy analysis method for solving systems. Some criteria are suggested for convergence of the series 8, in 5. Homotopy perturbation method for solving highly nonlinear. Mar 31, 2016 in this article, we focus on linear and nonlinear fuzzy volterra integral equations of the second kind and we propose a numerical scheme using homotopy perturbation method hpm to obtain fuzzy approximate solutions to them. Rabbani and others published new homotopy perturbation method to solve nonlinear problems find, read and cite all the research you need on researchgate. To facilitate the benefits of this proposal, an algorithmic form of the hpm is also designed to handle the same. This method is named by aboodh transform which is a combination of the new integral transform aboodh transform and the homotopy perturbation method. Homotopy perturbation method for free vibration analysis.
Based on numerical results, homotopy perturbation method convergence is illustrated. Application of the method for solving different kinds of differential equations can also be found in works 3234. Solving porous medium equation using aboodh transform. The homotopy perturbation technique does not depend upon a small parameter in the equation. However, we develop a method to obtain the proper decomposition of f x, y which lets us obtain the solution with minimum computation and accelerate the convergence of the solution. One of the most powerful among these analytical methods is. Application of hes homotopy perturbation method for. In recent years, the homotopy perturbation method hpm has been employed to. Homotopy perturbation method research papers academia.
The laplace homotopy analysis method lham is a combination of ham and laplace transform. The effectiveness of this method is demonstrated by finding the exact solutions of the fractional equations proposed, for the special case when. Research article modified homotopy perturbation method for solving fractional differential equations a. Next we consider the test example when the exact solution of the model is known, in order to approbate the hpm in cosmology. Siddiqi and iftikhar siddiqi and iftikhar, 20 presented the solution of higher order boundary value problems using the homotopy analysis method. Homotopy perturbation method is a novel approach that provides an approximate analytical solution to differential equations in the form of an infinite power series. The analytical results obtained by using ham are compared with those of hpm, mhpm. 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. The nonlinear termin the porous medium equationscan be easily handled by homotopy perturbation method and some cases of these equations. Homotopy perturbation method for free vibration analysis of. Index terms homotopy perturbation method hpm, partial differential.
This paper compares the homotopy perturbation method hpm with finite difference method for solving these equations. In the present paper, we study a homogeneous cosmological model in friedmannrobertsonwalker frw spacetime by means of the socalled homotopy perturbation method hpm. Application of hes homotopy perturbation method for solving. This method di ers from previous homotopy and continuation methods in that its aim is to nd a minimizer for each of a set of values of the homotopy parameter, rather than to follow a path of minimizers. In section 4, we introduce application of hpm for lp under unrestricted variables with some examples. Second, the ham is a unified method for the lyapunov artificial small parameter method, the delta expansion method, the adomian decomposition method, and the homotopy perturbation method. Homotopy perturbation method is used for solving the multipoint boundary. This problem is solved using new approach in homotopy perturbation method appendix b. Application of homotopy analysis method for solving. One of the most powerful among these analytical methods is the homotopy perturbation method, which. Homotopy perturbation transform method for nonlinear differential. Akram and hamood, 20b find the solution of a class of sixth order boundary. 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 application of homotopy perturbation method hpm for solving systems of linear equations is further discussed and focused on a method for choosing an auxiliary matrix to improve the rate of convergence.
Thus, the main goal of this work is to apply the homotopy perturbation method hpm for solving linear and nonlinear manuscript received january 05, 20. Homotopy perturbation method to solve heat conduction. By combining the variational iteration method and the homotopy perturbation method, this technique possesses a fast convergence rate with high accuracy. The galerkins method is utilized to decrease the nonlinear partial differential equation to a nonlinear secondorder ordinary differential equation. Pdf convergence analysis of homotopy perturbation method. Analytical solutions and frequency factors are evaluated for different ratios of axial load n acting on the beam to euler buckling load, n r.
Pdf new homotopy perturbation method to solve nonlinear. The essential idea of this method is to introduce a homotopy parameter, say p, which takes the values from 0 to 1. Yen2, shirin noei3 and hamidreza ramezanpour4 1,2department of electrical engineering florida international university, miami, florida, usa a. Homotopy perturbation method for linear programming problems. The combination of the perturbation method and the homotopy method is called the homotopy perturbation method hpm, which has eliminated the limitations of the traditional perturbation methods. This work presents the homotopy perturbation transform method for nonlinear fractional partial differential equations of the caputofabrizio fractional operator. How ever, the existing methods such as adomian decomposi tion method, variational iteration method and homotopy perturbation method involve the computation of ado mian polynomials, and the integral related with e.
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