Symmetry analysis and conservation laws of some third-order difference equations

Mamba, S.; Folly-Gbetoula, Mensah; Kara, A. H.

doi:10.1080/10236198.2017.1382486

Cited by 7 publications

(6 citation statements)

References 7 publications

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“…In fact, substituting l � 1, k � 2, a � 1 and b � ± 1 in (33), we obtain results in eorems 1 and 3 by Ibrahim in [15]. Substituting l � 1, k � 2, a n � a and b n � b in (32), we obtain the results in [12]. Substituting l � 2, k � 2, a n � ± 1 and b n � ± 1 in (33), we obtain results in eorems 1, 4, 6, and 9 in [8].…”

Section: Resultssupporting

confidence: 52%

“…is paper is a generalization of some work in [8,9,[12][13][14][15][16][17]. In fact, substituting l � 1, k � 2, a � 1 and b � ± 1 in (33), we obtain results in eorems 1 and 3 by Ibrahim in [15].…”

Section: Resultsmentioning

confidence: 59%

“…Lastly, it is worth indicating that some of the results in [8,9,15] have been studied in a more general setting by Folly-Gbetoula and Nyirenda in [12][13][14]16].…”

Section: Resultsmentioning

confidence: 99%

“…Special cases of (4) attracted the interest of many researchers and interesting results can be found in the literature, see [7][8][9][10][11][12][13][14][15][16][17] among others. In this paper, we generalize some results in these articles by studying (2) with initial values x 0 , x 1 , .…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On a Study of a Family of Higher-Order Recurrence Relations

Folly-Gbetoula

Mkhwanazi

Nyirenda

2022

Mathematical Problems in Engineering

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In this work, group theory is applied to obtain generators of the Lie algebra for a class of rational difference equations of order k + l where k and l are positive integers. This is followed by deriving invariants and solutions via some linear recurrences and with the introduction of some number-theoretic arithmetical functions. Furthermore, sufficient conditions for the existence of solutions for periods two and four are provided in special cases. The results in this paper generalize certain known results.

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Section: Resultssupporting

confidence: 52%

Section: Resultsmentioning

confidence: 59%

“…Lastly, it is worth indicating that some of the results in [8,9,15] have been studied in a more general setting by Folly-Gbetoula and Nyirenda in [12][13][14]16].…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On a Study of a Family of Higher-Order Recurrence Relations

Folly-Gbetoula

Mkhwanazi

Nyirenda

2022

Mathematical Problems in Engineering

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“…The obtained results encourage further attempts to understand connections of stability and continuous symmetries for difference schemes in general cases, for example, two-and three-dimensional cases of multiphase flow equations in porous media. Moreover, the question of conservation laws [29,30] is close to continuous symmetries and not discussed in this article. It can help in a wider understanding of problems, which are considered in the article.…”

Section: Generation Of Numerical Solutionsmentioning

confidence: 99%

Numerical Simulation Using Finite-Difference Schemes with Continuous Symmetries for Processes of Gas Flow in Porous Media

Марков

Rodionov

2019

Computation

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This article presents the applications of continuous symmetry groups to the computational fluid dynamics simulation of gas flow in porous media. The family of equations for one-phase flow in porous media, such as equations of gas flow with the Klinkenberg effect, is considered. This consideration has been made in terms of difference scheme constructions with the preservation of continuous symmetries, which are presented in original parabolic differential equations. A new method of numerical solution generation using continuous symmetry groups has been developed for the equation of gas flow in porous media. Four classes of invariant difference schemes have been found by using known group classifications of parabolic differential equations with partial derivatives. Invariance of necessary conditions for stability has been shown for the difference schemes from the presented classes. Comparison with the classical approach for seeking numerical solutions for a particular case from the presented classes has shown that the calculation speed is greater by several orders than for the classical approach. Analysis of the accuracy for the presented method of numerical solution generation on the basis of continuous symmetries shows that the accuracy of generated numerical solutions depends on the accuracy of initial solutions for generations.

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