Homotopy perturbation method for linear programming problems

Najafi, H. Saberi; Edalatpanah, S. A.

doi:10.1016/j.apm.2013.09.011

Cited by 11 publications

(6 citation statements)

References 15 publications

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“…This method, which is a combination of homotopy in topology and classic perturbation techniques, provides us with a convenient way to obtain analytic or approximate solutions for a wide variety of problems arising indifferent fields. In recent years, the application of the homotopy perturbation method in nonlinear problems has been developed by scientists and engineers (He 2003, 2006; Olga 2011; Ebaid 2014; Najafi and Edalatpanah 2014). …”

Section: The Approximate Analytic Solutions Of Eq (8) Based On the Hmentioning

confidence: 99%

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method

2016

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In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

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Section: The Approximate Analytic Solutions Of Eq (8) Based On the Hmentioning

confidence: 99%

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method

2016

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“…Allahviranloo et al [27][28][29][30] developed some important numerical schemes for solving a fuzzy linear system of equations (FLSEs). Moreover, certain methods to solve fuzzy linear systems have been discussed in [31][32][33][34]. Akram et al [35][36][37][38][39] studied certain schemes for solving the bipolar fuzzy linear system of equations.…”

Section: Introductionmentioning

confidence: 99%

LU Decomposition Scheme for Solving m-Polar Fuzzy System of Linear Equations

Koam

Akram

Muhammad

et al. 2020

Mathematical Problems in Engineering

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This paper presents a new scheme for solving m-polar fuzzy system of linear equations (m-PFSLEs) by using LU decomposition method. We assume the coefficient matrix of the system is symmetric positive definite, and we discuss this point in detail with some numerical examples. Furthermore, we investigate the inconsistent m×nm-polar fuzzy matrix equation (m-PFME) and find the least square solution (LSS) of this system by using generalized inverse matrix theory. Moreover, we discuss the strong solution of m-polar fuzzy LSS of the inconsistent m-PFME. In the end, we present a numerical example to illustrate our approach.

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“…HPM obtained the approximate solution not only for small parameters, but also for very large parameters and the initial approximation can be freely selected with possible unknown constants. In the literature, numerous authors have successfully applied HPM for various kind of problems such as inverse problem of diffusion equation [34], linear programming problems [32], blood flows problem [2], nonlinear oscillator problems [3,12,35,38,39], hybridization of HPM with Laplace transform [23,27], HPM with expanding parameter [17], HPM with auxiliary parameters [16], and a fractional calculus [18,22,36,37].…”

Section: Introductionmentioning

confidence: 99%

Solution of Newell-Whitehead-Segel equation by variational iteration method with He's polynomials

Nadeem¹,

Yao²,

Parveen³

2019

J. Math. Computer Sci.

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This article seeks to extend the variational iteration method (VIM) with He's polynomials for the approximate solution of nonlinear Newell-Whitehead-Segel equation (NWSE). Lagrange multiplier in correction functional is determined with the help of variational theory, and then homotopy perturbation method (HPM) is employed to dissolve the nonlinear terms. Thus a successful series is obtained with these iterations which are termed as He's polynomials. Result shows that this method is highly accurate and comes closer very quickly to the exact solution. We formulate three possible cases of NWSE to show the capability and ability of the present method. The valuable outcome discloses that the proposed strategy is very convenient, straightforward and can be utilized to linear and nonlinear problems.

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Homotopy perturbation method for linear programming problems

Cited by 11 publications

References 15 publications

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method

LU Decomposition Scheme for Solving m-Polar Fuzzy System of Linear Equations

Solution of Newell-Whitehead-Segel equation by variational iteration method with He's polynomials

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