On Construction of Finite-Dimensional Mathematical Model of Convection-Diffusion Process with Usage of the Petrov-Galerkin Method

Salnikov, Nikolay N.; Siryk, Sergii V.; Tereshchenko, I. A.

doi:10.1615/jautomatinfscien.v42.i6.50

Cited by 8 publications

(4 citation statements)

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“…Here, in particular, papers [26][27][28][29][30][31][32][33] address the application of ADM to various fractional transport models, whilst paper [34] discusses some nonstandard definitions of fractional derivatives. Sources [35][36][37][38] contain developments and/or reviews of various numerical approaches to transport problems, while [39] proposes an interesting perturbational approach to construct analytical approximations. Finally, the review paper [40] contains a comprehensive number of modern applications of fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Fractional-Order System of One-Dimensional Keller–Segel Equations: A Modified Analytical Method

Yasmin

Iqbal

2022

Symmetry

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In this paper, an analytical method is implemented to solve fractional-order Keller–Segel equations. The Yang transformation along with the Adomian decomposition method is implemented to obtain the solution of the given problems. The present method has an edge over other techniques as it does not need extra calculations and materials. The validity of the suggested technique is verified by considering some numerical problems. The results obtained confirm the better accuracy of the current technique. The suggested technique has a lesser number of calculations and is straightforward to apply and therefore can be applied to other fractional-order partial differential equations.

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Section: Introductionmentioning

confidence: 99%

Analysis of Fractional-Order System of One-Dimensional Keller–Segel Equations: A Modified Analytical Method

Yasmin

Iqbal

2022

Symmetry

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“…Papers [12][13][14] address the application of ADM to various fractional transport models. Finally, works [15][16][17][18][19][20] reflect some developments and reviews of various numerical approaches to transport problems.…”

Section: Introductionmentioning

confidence: 99%

A Reliable Way to Deal with Fractional-Order Equations That Describe the Unsteady Flow of a Polytropic Gas

et al. 2022

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In this paper, fractional-order system gas dynamics equations are solved analytically using an appealing novel method known as the Laplace residual power series technique, which is based on the coupling of the residual power series approach with the Laplace transform operator to develop analytical and approximate solutions in quick convergent series types by utilizing the idea of the limit with less effort and time than the residual power series method. The given model is tested and simulated to confirm the proposed technique’s simplicity, performance, and viability. The results show that the above-mentioned technique is simple, reliable, and appropriate for investigating nonlinear engineering and physical problems.

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“…The shallow water model can be seen as essentially a convection-diffusion-reaction model [30]. In this regard, Salnikov and Siryk [31][32][33] proposed the Petrov-Galerkin method, as well as the modification of the Petrov−Galerkin method, for constructing continuous piecewise polynomial weight functions in two and three-dimensional domains. A finite number of variable parameters associated with the edges of a grid partition determine the form of such functions.…”

Section: Introductionmentioning

confidence: 99%

Sawi Transform Based Homotopy Perturbation Method for Solving Shallow Water Wave Equations in Fuzzy Environment

Sahoo

Chakraverty

2022

Mathematics

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In this manuscript, a new hybrid technique viz Sawi transform-based homotopy perturbation method is implemented to solve one-dimensional shallow water wave equations. In general, the quantities involved with such equations are commonly assumed to be crisp, but the parameters involved in the actual scenario may be imprecise/uncertain. Therefore, fuzzy uncertainty is introduced as an initial condition. The main focus of this study is to find the approximate solution of one-dimensional shallow water wave equations with crisp, as well as fuzzy, uncertain initial conditions. First, by taking the initial condition as crisp, the approximate series solutions are obtained. Then these solutions are compared graphically with existing solutions, showing the reliability of the present method. Further, by considering uncertain initial conditions in terms of Gaussian fuzzy number, the governing equation leads to fuzzy shallow water wave equations. Finally, the solutions obtained by the proposed method are presented in the form of Gaussian fuzzy number plots.

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On Construction of Finite-Dimensional Mathematical Model of Convection-Diffusion Process with Usage of the Petrov-Galerkin Method

Cited by 8 publications

References 0 publications

Analysis of Fractional-Order System of One-Dimensional Keller–Segel Equations: A Modified Analytical Method

Analysis of Fractional-Order System of One-Dimensional Keller–Segel Equations: A Modified Analytical Method

A Reliable Way to Deal with Fractional-Order Equations That Describe the Unsteady Flow of a Polytropic Gas

Sawi Transform Based Homotopy Perturbation Method for Solving Shallow Water Wave Equations in Fuzzy Environment

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