共查询到20条相似文献,搜索用时 15 毫秒
1.
In this article, we have used the homotopy perturbation method (HPM) to find the travelling wave solutions for some non-linear initial-value problems in the mathematical physics. These problems consist of the Burgers–Fisher equation, the Kuramoto–Sivashinsky equation, the coupled Schordinger KdV equations and the long–short wave resonance equations together with initial conditions. The results of these problems reveal that the HPM is very powerful, effective, convenient and quite accurate to the systems of non-linear equations. It is predicted that this method can be found widely applicable in engineering and physics. 相似文献
2.
Talha Achouri Khaled Omrani 《Numerical Methods for Partial Differential Equations》2010,26(2):399-411
In this article, the homotopy perturbation method (HPM) is used to implement the modified regularized long‐wave (MRLW) equation with some initial conditions. The method is very efficient and convenient and can be applied to a large class of problems. In the last, three invariants of the motion are evaluated to determine the conservation properties of the system. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
3.
Mustafa Inc 《Numerical Methods for Partial Differential Equations》2010,26(5):1224-1235
In this article, we present the Homotopy Perturbation Method (Shortly HPM) for obtaining the numerical solutions of the Korteweg‐de Vries Burgers (KdVB) equation. The series solutions are developed and the reccurance relations are given explicity. The initial approximation can be freely chosen with possibly unknown constants which can be determined by imposing the boundary and initial conditions. The results reveal that HPM is very simple and effective. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
4.
Alev Kelleci Ahmet Yıldırım 《Numerical Methods for Partial Differential Equations》2011,27(4):982-995
In this study, we combined homotopy perturbation and Pade techniques for solving homogeneous and inhomogeneous two‐dimensional parabolic equation. Also, we apply our combined method for coupled Burgers' equations. The numerical results demonstrate that our combined method gives the approximate solution with faster convergence rate and higher accuracy than using the classic homotopy perturbation method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 982–995, 2011 相似文献
5.
The aim of this article is to construct a new efficient recurrent relation to solve nonlinear Burgers' equation. The homotopy perturbation method is used to solve this equation. Because Burgers' equation arises in many applications, it is worth trying new solution methods. Comparison of the results with those of Adomian's decomposition method leads to significant consequences. Four standard problems are used to illustrate the method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
6.
In this paper, we extend the homotopy perturbation method to solve the Davey-Stewartson equations. The homotopy perturbation
method is employed to compute an approximation to the solution of the equations. Computation the absolute errors between the
exact solutions of the Davey-Stewartson equations and the HPM solutions are presented. Some plots are given to show the simplicity
the method.
The article is published in the original. 相似文献
7.
Olga Martin 《Applied mathematics and computation》2011,217(21):8567-8574
The purpose of this paper consists in the finding of the solution for a stationary transport equation using the techniques of homotopy perturbation method (HPM). The results of a numerical example illustrate the accuracy and computational efficiency of the new proposed method. 相似文献
8.
In this paper, a boundary perturbation interior point homotopy method is proposed to give a constructive proof of the general Brouwer fixed point theorem and thus solve fixed point problems in a class of nonconvex sets. Compared with the previous results, by using the newly proposed method, initial points can be chosen in the whole space of Rn, which may improve greatly the computational efficiency of reduced predictor-corrector algorithms resulted from that method. Some numerical examples are given to illustrate the results of this paper. 相似文献
9.
Based on the modified homotopy perturbation method (MHPM), exact solutions of certain partial differential equations are constructed by separation of variables and choosing the finite terms of a series in p as exact solutions. Under suitable initial conditions, the PDE is transformed into an ODE. Some illustrative examples reveal the effciency of the proposed method. 相似文献
10.
Elçin Yusufoğlu Cevad Selam 《Numerical Methods for Partial Differential Equations》2010,26(6):1434-1442
In this article, to solve the modified equal width wave (MEW) equation, the homotopy analysis method (HAM) is proposed. The initial approximation can be freely chosen with possible unknown constant, which can be determined by using the boundary and initial conditions. The HAM contains the auxiliary parameter ?, which provides us to adjust and control the convergence region of solution series with a simple way. Three conservative quantities are reported. Numerical results show that this method is a promising and powerful tool to solve the MEW equation. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
11.
Z.Z. Ganji D.D. Ganji Ammar D. Ganji M. Rostamian 《Numerical Methods for Partial Differential Equations》2010,26(1):117-124
In this letter, we implement a relatively new analytical technique, the homotopy perturbation method (HPM), for solving linear partial differential equations of fractional order arising in fluid mechanics. The fractional derivatives are described in Caputo derivatives. This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations applied in engineering mathematics. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of HPM. He's HPM, which does not need small parameter is implemented for solving the differential equations. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants that can be determined by imposing the boundary and initial conditions. It is predicted that HPM can be found widely applicable in engineering. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
12.
The aim of this paper is to present an efficient and reliable treatment of the homotopy perturbation method (HPM) for two dimensional time-fractional wave equation (TFWE) with the boundary conditions. The fractional derivative is described in the Caputo sense. The initial approximation can be determined by imposing the boundary conditions. The method provides approximate solutions in the form of convergent series with easily computable components. The obtained results shown that the technique introduced here is efficient and easy to implement. 相似文献
13.
In this study, linear and nonlinear partial differential equations with the nonhomogeneous initial conditions are considered. We used Variational iteration method (VIM) and Homotopy perturbation method (HPM) for solving these equations. Both methods are used to obtain analytic solutions for different types of differential equations. Four examples are presented to show the application of the present techniques. In these schemes, the solution takes the form of a convergent series with easily computable components. The present methods perform extremely well in terms of efficiency and simplicity. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
14.
In this paper, we propose new technique for solving stiff system of ordinary differential equations. This algorithm is based on Laplace transform and homotopy perturbation methods. The new technique is applied to solving two mathematical models of stiff problem. We show that the present approach is relatively easy, efficient and highly accurate. 相似文献
15.
In this paper, He’s homotopy perturbation method is proposed to solve nth-order integro-differential equations. The results reveal that the method is very effective and simple. 相似文献
16.
Filiz Taşcan Mehmet Naci Özer 《Numerical Methods for Partial Differential Equations》2010,26(6):1522-1529
We performed adapted homotopy perturbation method on the Henon‐Heiles system with the help of the symbolic computation of package Maple 10 (User Manual by Maplesoft. www.maplesoft.com ). We obtained a new approximate solution of the Henon‐Heiles system. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 相似文献
17.
H. Jafari M. Saeidy M. A. Firoozjaee 《Numerical Methods for Partial Differential Equations》2010,26(5):1021-1032
In this article, higher dimensional initial boundary value problems of variable coefficients are solved by means of an analytic technique, namely the Homotopy analysis method (HAM). Comparisons are made between the Adomian decomposition method (ADM), the exact solution and the homotopy analysis method. The results reveal that the proposed method is very effective and simple. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
18.
This article presents the general case‐study of our previous works regarding generalized Boussinesq equations [17, 18, 19], that focus on application of various subordinate methods where are applied to construct more general exact solutions of the coupled Boussinesq equations. In this article, the ‐expansion method is applied on coupled Boussinesq equations. Our work is motivated by the fact that the ‐expansion method provides not only more general forms of solutions but also periodic, solitary waves, and rational solutions. The method appears to be easier and faster by means of a symbolic manipulation program. © 2016 Wiley Periodicals, Inc. Complexity 21: 151–155, 2016 相似文献
19.
Melda Duman 《Applied mathematics and computation》2010,216(2):492-1494
The asymptotic formulae for the eigenvalues and eigenfunctions of Sturm-Liouville problem with the Dirichlet boundary conditions when the potential is square integrable on [0, 1] are obtained by using homotopy perturbation method. 相似文献
20.
In this study, static pull-in instability of electrostatically-actuated microbridges and microcantilevers is investigated considering different nonlinear effects. Galerkin’s decomposition method is utilized to convert the nonlinear differential equations of motion to nonlinear integro-algebraic equations. Afterward, analytic solutions to static deflections of the microbeams are obtained using the homotopy perturbation method. Results are in excellent agreement with those presented in the literature. 相似文献