Antireduction and exact solutions of nonlinear heat equations

Fushchych, W. I.; Zhdanov, Renat

doi:10.2991/jnmp.1994.1.1.4

Cited by 58 publications

(60 citation statements)

References 2 publications

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“…Examples from the previous works are used. It is concluded that Adomian Decomposition Method provides both exact and approximate numerical solutions for the heat equations with nonlinear power in comparison to other solutions such as antireductiori method (Fushchych& Zhdanov, 1994) and Lie symmetry reduction method (Euler & Euler, 1997 …”

Section: Discussionmentioning

confidence: 99%

Adomian Decomposition Method for Solving the Nonlinear Heat Equation

Alhaddad¹

2017

IJERA

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This paper studies the application of the Adomian Decomposition Method to find the exact and approximate solutions of the heat equation with power nonlinearity. First, the relevant literature is studied in understanding the importance and extent of applicability of the method in the applied science. The literature review has been incorporated in the introduction of the paper. The rest of the paper is divided in three further sections. The first part Adomian Decomposition Method provides a step-by-step guide of applying the method on any heat equation with nonlinearity. The second section is labeled as Applications. It considers two examples from the previous works of Pumak (2005) and Hetmaniok et al. (2010) to find the exact and approximate solutions of the equations respectively.

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Section: Discussionmentioning

confidence: 99%

Adomian Decomposition Method for Solving the Nonlinear Heat Equation

Alhaddad¹

2017

IJERA

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“…We also have g 2 ∩ g 2 ∼ su(2) ⊕ su(2) ∼ so (4), from which we conclude that G 2 has no realizations by operators of the form (8) which are symmetry operators of (1).…”

Section: Theoremmentioning

confidence: 95%

“…if we take into account that the algebras so (3,2) and so(4, 1) contain so (3,1), and the algebra so(5) contains so (4).…”

Section: Theoremmentioning

confidence: 99%

“…The group classification of partial differential equations (PDEs) of mathematical physics is one of the corner stones of modern group analysis of differential equations [1][2][3][4][5][6][7][8][9][10] . This classification is of particular interest because it specifies the origin of possible applications of the powerful methods of Lie groups and algebras for the analysis and construction of solutions of equations which model physical processes and possess non-trivial symmetry properties.…”

Section: Introductionmentioning

confidence: 99%

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Preliminary group classification of quasilinear third-order evolution equations

Huang

Zhang

2009

Appl. Math. Mech.-Engl. Ed.

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Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six nonequivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.

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“…The classical method for finding symmetry reductions of PDEs is the Lie group method of infinitesimal transformations [13][14][15]. Several generalizations to the classical method have been introduced, these include the nonclassical method [16], the direct method [17][18][19][20] and the generalized conditional symmetry method [21][22][23][24][25]. The symmetry related methods have been successfully applied to seek exact solutions and symmetry reductions of nonlinear PDEs.…”

Section: Introductionmentioning

confidence: 99%