Approximate solutions to shallow water wave equations by the homotopy perturbation method coupled with Mohand transform

Liu, Yue; Zhang, Yanni; Pang, Jun

doi:10.3389/fphy.2022.1118898

Cited by 3 publications

(3 citation statements)

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“…al. [11] on the otherhand employ homotopy perturbation method for solving the 2D shallow water equations. For numerically solving the different nonlinear equations, mostly variants of the finite volume method are used (Yang et.…”

Section: Introductionmentioning

confidence: 99%

On the existence of flux as a function of the surface elevation for long wave solution of shallow water equations

Bose,

Gorain

2024

Electron. J. Appl. Math.

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The shallow water equations in mechanics of fluids, govern the motion of a shallow layer of water over a fixed impervious bed. In this paper, the bed form is assumed to be rough and horizontal, and the motion of water is assumed to be of the long wave type (Lamb [1], pp. 254-256) such that the free surface has a gradually varying propagating profile. Gravitation permits such motion but is resisted by the turbulence generated by the bed friction. A model of the governing equations based on the Reynolds averaged Navier-Stokes equations has recently been given by Bose [2], which is highly nonlinear. A heuristic approach of numerically solving the equations for the modified long waves is also presented in that article, by assuming that the horizontal flux across a section of flow is some function of the free surface elevation alone. This key assertion is analysed in this article and proved to hold provided some boundedness criteria are satisfied by the flux gradients. The theory is apparently applicable to find appropriate boundedness conditions on the flux of flow for numerically solving long wave equations in the case of other models for long wave propagation as well.

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Section: Introductionmentioning

confidence: 99%

On the existence of flux as a function of the surface elevation for long wave solution of shallow water equations

Bose,

Gorain

2024

Electron. J. Appl. Math.

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“…Laplace transform [33], Elzaki transform [34], Aboodh transform [35], Kushare transform [36], and Mohand transform [37] are some of them. He-Mohand method [38] is the modification of HPM with Mohand transform. This transform was introduced by Mohand [37] in 2017 to solve differential equations.…”

Section: Introductionmentioning

confidence: 99%

Time-fractional lorenz type chaotic systems with asymmetric gaussian uncertainty: series solutions via extended He-Mohand algorithm in fuzzy-caputo sense

Qayyum,

Ahmad

2024

Phys. Scr.

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In this paper, modeling and analysis of 3D fuzzy-fractional Lorenz type systems is presented. System under-consideration includes classical Lorenz, Chen and Burke-Shaw chaotic systems. Asymmetrical Gaussian fuzzy logic with fractional calculus is applied to model complex systems with intricate patterns. The focus of this study is fuzzy-fractional modeling and simulations. For solution purpose, a hybrid perturbation method is introduced where standard homotopy perturbation method (HPM) is enhanced by incorporating Mohand transform in fuzzy-Caputo sense. This hybrid mechanism provides an efficient way to find solutions in fuzzy-fractional environment. Validity of obtained solutions is checked by computing residual errors, which ultimately confirms the convergence of applied methodology. The dynamical behavior of fuzzy-fractional chaotic models is analyzed through various 2-3D plots to represent the chaotic regions as well unpredictable trajectories at both upper and lower bounds. Fuzzy membership functions of 3D models at different values of fractional derivative are also demonstrated through 2D plots. Analysis reveals that extended hybrid methodology proves to be a valuable tool for researchers dealing with nonlinear chaotic fractional systems with fuzzy characteristics.

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“…Te Chebyshev spectral method was utilized by Kumar et al [50] to analyze the fuzzy-fractional Fredholm-Volterra integrodiferential equation. A powerful tool to solve nonlinear fractional diferential equations in fuzzy form is the He-Mohand method [51]. It is an efcient technique that provides a practical method for solving diferential models by combining the homotopy perturbation technique (HPM) and the Mohand transform.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of the Fuzzy-Fractional Chaotic Financial System Using the Extended He–Mohand Algorithm in a Fuzzy-Caputo Sense

Qayyum,

Ahmad,

Tahir

et al. 2023

International Journal of Intelligent Systems

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This paper contains modeling of a fuzzy-fractional financial chaotic model based on triangular fuzzy numbers (TFNs) to predict the idea that long-term dependency and uncertainty both have an impact on the financial market. For solution purposes, the He–Mohand algorithm is proposed where homotopy perturbation is hybrid with Mohand transform in a fuzzy-Caputo sense. In analysis, solutions and corresponding errors at upper and lower bounds are estimated. The obtained numerical results are displayed in tables to show the reliability and efficiency of the proposed methodology. Upper bound errors range from 10 − 6 to 10 − 12 and lower bound errors from 10 − 6 to 10 − 11 . For graphical analysis, system profiles are illustrated as two-dimensional and three-dimensional plots at diverse values of fractional parameters and time to comprehend the physical behavior of the proposed fuzzy-fractional model. These plots demonstrate that the interest rate, price index, and investment demand decrease with the increase of the value of the r -cut at the lower bound. At the upper bound, this behavior is totally opposite. The chaotic behavior of the system at smaller values of saving rate, elasticity of demands, and per-investment cost is greater in contrast to their larger value. Analysis reveals that the proposed methodology (He–Mohand algorithm) provides a new way of understanding the complicated structure of financial systems and provides new insights into the dynamics of financial markets. This algorithm has potential applications in risk management, portfolio optimization, and trading strategies.

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Approximate solutions to shallow water wave equations by the homotopy perturbation method coupled with Mohand transform

Cited by 3 publications

References 32 publications

On the existence of flux as a function of the surface elevation for long wave solution of shallow water equations

On the existence of flux as a function of the surface elevation for long wave solution of shallow water equations

Time-fractional lorenz type chaotic systems with asymmetric gaussian uncertainty: series solutions via extended He-Mohand algorithm in fuzzy-caputo sense

Modeling and Analysis of the Fuzzy-Fractional Chaotic Financial System Using the Extended He–Mohand Algorithm in a Fuzzy-Caputo Sense

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