Elzaki Transform Homotopy Perturbation Method for Solving Gas Dynamics Equation

Kiran, Prem; Bhadane, G Prem Kiran; Pradhan, V. H.

doi:10.15623/ijret.2013.0212045

Cited by 7 publications

(1 citation statement)

References 3 publications

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“…Beberapa implementasi metode pertubasi homotopi transformasi Elzaki pada beberapa persoalan nilai awal, seperti : persamaan diferensial parsial nonlinear (Elzaki & Hilal, 2012), persamaan Sine-Gorden dan Klein-Gorden (Hesameddini & Abdollahy, 2013), Sistem persamaan parsial nonlinear (Elzaki & Biazar, 2013), persamaan dinamika gas (Bhadane & Pradhan, 2013), persamaan Burger (Suleman et al, 2016), persamaan diferensial fraksional nonlinear (Singh & Sharma, 2020).…”

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Penyelesaian Persamaan Diferensial Abelian Menggunakan Metode Perturbasi Homotopi Transformasi Elzaki

Wartono

2021

jmpm j. mat. dan pendidik. mat.

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Metode transformasi Elzaki perturbasi homotopi merupakan salah satu metode semi analitik yang dikonstruksi menggunakan kombinasi metode transformasi Elzaki dan metode perturbasi homotopi. Metode ini digunakan untuk menyelesaikan persamaan diferensial, baik linear maupun nonlinear dalam bentuk deret polinomial. Artikel ini membahas penyelesaian persamaan diferensial Abelian jenis pertama menggunakan metode perturbasi homotopi transformasi Elzaki. Simulasi numerik diberikan untuk menguji konvergensi penyelesaian hampiran dengan menggunakan dua contoh. Hasil kajian menunjukkan bahwa metode tersebut dapat menyelesaikan persamaan diferensial Abelian. Nilai-nilai penyelesaian hampiran juga di plot dalam bentuk grafik untuk beberapa jumlah suku-suku solusi hampiran. Hasil plot menunjukkan bahwa pola kurva yang dibentuk cenderung teratur.

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Penyelesaian Persamaan Diferensial Abelian Menggunakan Metode Perturbasi Homotopi Transformasi Elzaki

Wartono

2021

jmpm j. mat. dan pendidik. mat.

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The Fractional View Analysis of Polytropic Gas, Unsteady Flow System

Khan

Islam

Arif

2021

Mathematical Problems in Engineering

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Generally, the differential equations of integer order do not properly model various phenomena in different areas of science and engineering as compared to differential equations of fractional order. The fractional-order differential equations provide the useful dynamics of the physical system and thus provide the innovative and effective information about the given physical system. Keeping in view the above properties of fractional calculus, the present article is related to the analytical solution of the time-fractional system of equations which describe the unsteady flow of polytropic gas dynamics. The present method provides the series form solution with easily computable components and a higher rate of convergence towards the targeted problem’s exact solution. The present techniques are straightforward and effective for dealing with the solutions of fractional-order problems. The fractional derivatives are expressed in terms of the Caputo operator. The targeted problems’ solutions are calculated using the Adomian decomposition method and variational iteration methods along with Shehu transformation. In the current procedures, we first applied the Shehu transform to reduce the problems into a more straightforward form and then implemented the decomposition and variational iteration methods to achieve the problems’ comprehensive results. The solution of the nonlinear equations of unsteady flow of a polytropic gas at various fractional orders of the derivative is the core point of the present study. The solution of the proposed fractional model is plotted via two- and three-dimensional graphs. It is investigated that each problem’s solution-graphs are best fitted with each other and with the exact solution. The convergence of fractional-order problems can be observed towards the solution of integer-order problems. Less computational time is the major attraction of the suggested methods. The present work will be considered a useful tool to handle the solution of fractional partial differential equations.

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Analytical and Approximate Solutions of the Nonlinear Gas Dynamic Equation Using a Hybrid Approach

Nadeem

Ali

2023

Journal of Mathematics

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This paper presents the study of a numerical scheme for the analytical solution of nonlinear gas dynamic equation. We use the idea of Laplace–Carson transform and associate it with the homotopy perturbation method (HPM) for obtaining the series solution of the equation. We show that this hybrid approach is excellent in agreement and converges to the exact solution very smoothly. Further, HPM combined with He’s polynomial is utilized to minimize the numerical simulations in nonlinear conditions that make it easy for the implementation of Laplace–Carson transform. We also exhibit a few graphical solutions to indicate that this approach is extremely reliable and convenient for linear and nonlinear challenges.

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Elzaki Transform Homotopy Perturbation Method for Solving Gas Dynamics Equation

Abstract: In this paper, the ELzaki transform homotopy perturbation method (ETHPM)

Cited by 7 publications

References 3 publications

Penyelesaian Persamaan Diferensial Abelian Menggunakan Metode Perturbasi Homotopi Transformasi Elzaki

Penyelesaian Persamaan Diferensial Abelian Menggunakan Metode Perturbasi Homotopi Transformasi Elzaki

The Fractional View Analysis of Polytropic Gas, Unsteady Flow System

Analytical and Approximate Solutions of the Nonlinear Gas Dynamic Equation Using a Hybrid Approach

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