2010
DOI: 10.1016/j.camwa.2010.01.039
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Numerical study of the solution of the Burgers and coupled Burgers equations by a differential transformation method

Abstract: a b s t r a c tIn this paper, the Differential Transformation Method (DTM) is employed to obtain the numerical/analytical solutions of the Burgers and coupled Burgers equations. We begin by showing how the differential transformation method applies to the linear and nonlinear parts of any PDE and give some examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equations. We also compare it against three famous methods, namely the homotopy perturbation method, the h… Show more

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Cited by 110 publications
(71 citation statements)
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“…Later, Hassan (2008) had used this method to solve linear and non-linear system of differential equations. Due to its popularity in solving various types of equation, many authors had used the DTM to solve difference equations (Arikoglu & Ozkol 2006), fractional differential equations (Arikoglu & Ozkol 2007;Momani et al 2008), volterra integral equations (Odibat 2008;Tari et al 2009), integro-differential equations of fractional order (Nazari & Shahmorad 2010), Burgers and Schrödinger equations (Abazari & Borhanifar 2010;Borhanifar & Abazari 2011), fractional chaotic dynamical systems (Alomari 2011) and partial differential equations of order four (Soltanalizadeh & Branch 2012). These contributions showed that the DTM is widely used to solve many types of differential equation as stated.…”
Section: Introductionmentioning
confidence: 99%
“…Later, Hassan (2008) had used this method to solve linear and non-linear system of differential equations. Due to its popularity in solving various types of equation, many authors had used the DTM to solve difference equations (Arikoglu & Ozkol 2006), fractional differential equations (Arikoglu & Ozkol 2007;Momani et al 2008), volterra integral equations (Odibat 2008;Tari et al 2009), integro-differential equations of fractional order (Nazari & Shahmorad 2010), Burgers and Schrödinger equations (Abazari & Borhanifar 2010;Borhanifar & Abazari 2011), fractional chaotic dynamical systems (Alomari 2011) and partial differential equations of order four (Soltanalizadeh & Branch 2012). These contributions showed that the DTM is widely used to solve many types of differential equation as stated.…”
Section: Introductionmentioning
confidence: 99%
“…The analytic solution of the coupled nonlinear Burger's equation involving various transformation techniques are given by Fletcher [4], Abazari and Borhanifar [5] and Ablowitz and Clarkson [6]. Other powerful methods of arriving at exact solutions include the homotopy perturbation method, Hirota's bilinear method (Hirota [7]), and the delta method (Bender et al [8]).…”
Section: Introductionmentioning
confidence: 99%
“…Various methods proposed to solve nonlinear equations, including the Backiund transformation [8], Inverse method [3] Wronskian determinant technique [5], Numerical methods [4,2], Hirota bilinear method [6]. There are other methods like Jacobi elliptic function method [7], homotopy perturbation method [9].…”
Section: Introductionmentioning
confidence: 99%