Application of the (-expansion method for the generalized Fisher‘s equation and modified equal width equation

Taha, Wafaa M.; Noorani, Mohd Salmi Md

doi:10.1016/j.jaubas.2013.05.006

Cited by 9 publications

(8 citation statements)

References 42 publications

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“…For example, travailing wave variables in travelling wave solution of non-linear PDEs. numerous methods to find exact solution of nonlinear PDFs, have been suggested in the literature like: the tanh-coth method [1,2], sine-cosine method [3], homogeneous balance method [4,5], exp-function method [6], first-integral method [7], Jacobi elliptic function method [8], and (𝐺 ′ /𝐺)-Expansion method [9,10,11]. The standard method offered by Malfliet [12] is a strong technique to compute exact traveling waves solutions of non-linear partial differential equations, we will utilize the standard tanh method to find the traveling wave for a nonlinear diffusionconvection equation for different values of m and n [13,14,15].…”

Section: -Introductionmentioning

confidence: 99%

New traveling wave solutions of a nonlinear diffusion–convection equation by using standard tanh method

Aziz¹,

Taha²,

Hameed³

et al. 2023

Tikrit J. Pure Sci.

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Exact solutions of traveling wave are acquired by employ a relatively new technique which is called standard tanh method for a nonlinear diffusion–convection equation. The tanh method is applied for the first time for finding travelling wave solutions for the nonlinear diffusion–convection equation , where n and m, are integers, and , of order (m=4, n=7) and (m=5, n=9). Analytical solutions of a nonlinear diffusion–convection equations are obtained as a polynomial in tanh(x), and the plots for exact solutions are given. The obtained results are compared with F-Expansion method to validate the proposed approach.

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Section: -Introductionmentioning

confidence: 99%

New traveling wave solutions of a nonlinear diffusion–convection equation by using standard tanh method

Aziz¹,

Taha²,

Hameed³

et al. 2023

Tikrit J. Pure Sci.

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“…Taghizadeh [7] has applied the modified simple equation method. Taha and Noorani [8] have developed the G ′ /Gexpansion method. Rui et al [9] have used integral bifurcation method.…”

Section: Introductionmentioning

confidence: 99%

Numerical Calculations of the MEW Equation from a New Perspective

Karta

KUTLUAY²

2022

Preprint

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Numerical computations for natural systems and acquiring travelling wave solutions of nonlinear wave equations in relation to sciences such as optics, fluid mechanics, solid state physics, plasma physics, kinetics, and geology have become very important in the field of mathematical modeling recently. For this, many methods have been suggested. The strategy applied for this article is to obtain more perfect numerical solutions of Modified Equal Width equation (MEW), which is one of the equations used to model the nonlinear phenomena mentioned. For this purpose, the Lie-Trotter splitting technique is applied to the MEW equation. Firstly, the problem is split into two sub-problems, one linear and the other nonlinear, containing derivative with respect to time. Secondly, each subproblem is reduced to the algebraic equation system by using collocation finite element method (FEM) based on the quintic B-spline approximate functions for spatial discretization and the convenient classical finite difference approaches for temporal discretization. Then, the obtained systems are solved with the Lie Trotter splitting algorithm. Explanatory test problems are considered, showing that the newly proposed algorithm has superior accuracy than previous methods, and the numerical results produced by the proposed algorithm are shown in tables and graphs. In addition, the stability analysis of the new approach is examined. Therefore, it is appropriate to state that this new technique can be easily applied to partial differential equations used in other disciplines in terms of the results obtained and the cost of Matlab calculation software.

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“…In the literature, one can find out that the MEW equation has been solved analytically by several scholars. Among others, while Jin 2 used homotopy perturbation method, Taha and Noorani 3 implemented the G′/G‐expansion method, Rui et al 4 utilized integral bifurcation method, Luet al 5 used extend simple equation method, Lu 6 used He's variational iteration method, Wang et al 7 used dynamical system method, Wazwaz 8 used the sine‐cosine and tanh methods, Taghizadeh et al 9 used modified simple equation method. The nonlinear MEW equation is also solved by many numerical methods, among others; lumped Galerkin method, 10,11 operator splitting method, 12 finite difference method, 13,14 multigrid method, 15 subdomain method, 16,17 Petrov‐Galerkin method, 18,19 Fourier Pseudo‐Spectral Method 20 and collocation method 21–25 .…”

Section: Introductionmentioning

confidence: 99%

A new perspective for the numerical solution of the Modified Equal Width wave equation

Başhan

Yağmurlu

Uçar

et al. 2021

Math Methods in App Sciences

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Finding the approximate solutions to natural systems in the branch of mathematical modelling has become increasingly important and for this end various methods have been proposed. The purpose of the present paper is to obtain and analyze the numerical solutions of Modified Equal Width equation (MEW). This equation is one of those equations used to model nonlinear phenomena which has a significant role in several branches of science such as plasma physics, fluid mechanics, optics and kinetics. Firstly, for the discretization of spatial derivatives, a fifth‐order quintic B‐spline based scheme is directly implemented. Secondly, a forward finite difference formula is applied for the temporal discretization of derivatives with respect to time. Simulation results establish the validity and applicability of the suggested technique for a wide range of nonlinear equations. Then, the newly obtained theoretical consequences are numerically justified by the simulations and test problems. These illustrative test problems are presented verifying the superiority of the newly presented scheme compared to other existing schemes and techniques. The suggested method with symbolic computational software such as, Matlab, is proven as an effective way to obtain the soliton solutions of several nonlinear partial differential equations (PDEs). Finally, the newly obtained results are presented graphically to justify the approximate findings.

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Application of the (-expansion method for the generalized Fisher‘s equation and modified equal width equation

Cited by 9 publications

References 42 publications

New traveling wave solutions of a nonlinear diffusion–convection equation by using standard tanh method

New traveling wave solutions of a nonlinear diffusion–convection equation by using standard tanh method

Numerical Calculations of the MEW Equation from a New Perspective

A new perspective for the numerical solution of the Modified Equal Width wave equation

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