Lagrangian approach to a generalized coupled Lane–Emden system: Symmetries and first integrals

Muatjetjeja, Ben; Khalique, Chaudry Masood

doi:10.1016/j.cnsns.2009.06.002

Cited by 20 publications

(13 citation statements)

References 30 publications

(19 reference statements)

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“…Several cases arise and are presented in Tables 1, 2, 3, and 4. The Noether symmetries given in [6] from (25) to (44) always form a proper subalgebra of the Lie algebra that is obtained above. This can be seen from Tables 1, 2, 3, and 4.…”

Section: Principal Lie Algebra and Lie Group Classificationmentioning

confidence: 93%

“…It is worth mentioning that Wong [5], in his review paper of 1975, presented more than 140 references on this topic. A natural extension of (1), called the generalized Lane-Emden system [6], is given by…”

Section: Introductionmentioning

confidence: 99%

“…In [6] the authors studied Noether operators with respect to the standard Lagrangian of the generalized coupled Lane-Emden system (2). They obtained seven cases out of which six cases resulted in Noether point symmetries.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Group Classification of a Generalized Lane-Emden System

Muatjetjeja

Khalique

Mahomed

2013

Journal of Applied Mathematics

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Section: Principal Lie Algebra and Lie Group Classificationmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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Group Classification of a Generalized Lane-Emden System

Muatjetjeja

Khalique

Mahomed

2013

Journal of Applied Mathematics

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“…The non-linear stretching sheet problems are still to difficult to solve either numerically or theoretically. Many different types of numerical and analytical methods have been proposed to deal with complex geometries, like finite element time domain methods (FETDMs) (Elmkies and Joly, 1997), the discontinuous Galerk in methods (DGM) methods (König et al, 2010), the Adomian decomposition method (Šmarda and Archalousova, 2010;DiblÍk et al, 2010), the homotopy perturbation method (Slota, 2010(Slota, , 2011Hetmaniok et al, 2012;Ghorbani and Saberi-Nadjafi, 2007), the variational iteration method (Wazwaz, 2007;He et al, 2010;Turkyilmazoglu, 2011c), the homotopy analysis method (Turkyilmazoglu, 2011b, d;Ellahi and Zeeshan, 2011), the Lie group method (Muatjetjeja and Khalique, 2010), the homotopy perturbation transform method Khan and Mohyud-Din, 2010) and the other analytical methods (He, 2006). One of those solution methods is the Laplace decomposition method (LDM) was proposed by Khuri (2001) and developed by Yusufoglu (2006).…”

Section: Introductionmentioning

confidence: 99%

A novel Laplace decomposition method for non-linear stretching sheet problem in the presence of MHD and slip condition

Khan

2013

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose -This paper aims to suggest a novel modified Laplace decomposition method (MLDM) for MHD flow over a non-linear stretching sheet with slip condition by suitable choice of an initial solution. Design/methodology/approach -The governing partial differential equations are converted into dimensionless non-linear ordinary differential equation by similarity transformation, which is solved by MLDM. The method is based on the application of Laplace transform to boundary layers in fluid mechanics. The non-linear term can be easily handled by the use of He's polynomials. Findings -The series solution of the MHD flow of an incompressible viscous fluid over a non-linear stretching sheet subject to slip condition is obtained. An excellent agreement between the MLDM and HPM is achieved. Convergence of the obtained series solution is properly checked by using the ratio test. Practical implications -Stretching surface is an important type of flow occurring in a number of engineering processes such as heat-treated materials travelling between a feed roll and a wind up roll, aerodynamic extrusion of plastic sheets, glass fiber and paper production, cooling of an infinite metallic plate in a cooling path, manufacturing of polymeric sheets are few examples of flow due to stretching surfaces. This work provides a very useful source of information for researchers on this subject. Originality/value -Such flow analysis is even not available yet for the hydrodynamic fluid. The series solution for MHD boundary layer problem with slip condition by means of MLDM is yet not available in the literature.

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“…It is worth mentioning that the proposed method can be extended for solving systems of ordinary differential equations of EmdenFowler type as follows [23] …”

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confidence: 99%

A modified Adomian decomposition method for singular initial value Emden-Fowler type equations

Biazar

Hosseini

2016

IJAMR

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Traditional Adomian decomposition method (ADM) usually fails to solve singular initial value problems of Emden-Fowler type. To overcome this shortcoming, a new and effective modification of ADM that only requires calculation of the first Adomian polynomial is formally proposed in the present paper. Three singular initial value problems of Emden-Fowler type with , 1 α  , 2 and , 2  and have been selected to demonstrate the efficiency of the method.

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Lagrangian approach to a generalized coupled Lane–Emden system: Symmetries and first integrals

Cited by 20 publications

References 30 publications

Group Classification of a Generalized Lane-Emden System

Group Classification of a Generalized Lane-Emden System

A novel Laplace decomposition method for non-linear stretching sheet problem in the presence of MHD and slip condition

A modified Adomian decomposition method for singular initial value Emden-Fowler type equations

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