A variational iteration method (VIM) for nonlinear dynamic response of a cracked plate interacting with a fluid media

Motaharifar, F.; Ghassabi, M.; Talebitooti, Roohollah

doi:10.1007/s00366-020-00998-w

Cited by 15 publications

(10 citation statements)

References 54 publications

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“…The advantages of fractional derivatives become apparent in modelling mechanical and electrical properties of real materials, as well as in the description of rheological properties of rocks, and in many other fields. Most nonlinear fractional differential equations have no exact solution, so the approximate solution or numerical solution may be a good choice [24]. Related to this topic, we may refer the readers to [25][26][27] and the references therein.…”

Section: Application To Nonlinear Fractional Differential Equationmentioning

confidence: 99%

Estimating Fixed Points via New Iterative Scheme with an Application

Jubair

Ali

Kumar

2022

Journal of Function Spaces

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In this paper, we introduce a new scheme and prove convergence results for nonexpansive mappings as well as for weak contractions in the frame of Banach spaces. Moreover, we prove analytically and numerically that the proposed scheme converges to a fixed point of a weak contraction faster than some known and leading schemes. Further, we prove that the new scheme is almost stable with respect to weak contraction. For supporting the main results, we give a couple of nontrivial numerical examples, and the visualization is shown by using the Matlab program. Finally, the solution of a nonlinear fractional differential equation is approximated by operating the main result of the paper.

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Section: Application To Nonlinear Fractional Differential Equationmentioning

confidence: 99%

Estimating Fixed Points via New Iterative Scheme with an Application

Jubair

Ali

Kumar

2022

Journal of Function Spaces

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“…The numerical and artificial neural network simulation of unsteady hydromagnetic Williamson fluid flow in a radiative surface was investigated by Shafiq, A., et al [ 37 ]. Motahari far et al [ 38 ] investigated the nonlinear vibration of an isotropic cracked plate in an air cavity using variational iteration (VIM).…”

Section: Introductionmentioning

confidence: 99%

Variational iteration method along with intelligent computing system for the radiated flow of electrically conductive viscous fluid through porous medium

Shoaib¹,

Shah²,

Nisar³

et al. 2023

Heliyon

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“…Due to the flexibility and ability, the VIM has emerged as a promising tool to solve non-linear or complex systems. Consequently, this method was successfully implimented to find the approximate solution of Hilfer fractional advection diffusion equations with power law initial condition [2], of reaction diffusion system with fast reversible reaction [1], of wave-like and heat-like equations in large domains [9], of delay differential equations [10], of nonlinear singular boundary value problems [16], of the time fractional Fornberg-Whitham equation [25], of Burger's flow with fractional derivatives [28], of non-isothermal reaction diffusion model equations in a spherical catalyst [26], of Optical bright and dark soliton solutions for coupled nonlinear Schrdinger (CNLS) equations [27], to Bratu-like equation arising in electrospinningand [12], to free vibration analysis of a tapered beam mounted on two-degree of freedom subsystems [8] and to others [7,20,21,22]. The paper is organized as follows: The continuous model problem is defined in Section 2.…”

Section: Introductionmentioning

confidence: 99%

An Iterative Analytic Approximation for a Class of Non-Linear Singularly Perturbed Parabolic Partial

Khari

Kumar

2022

Preprint

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In this article, a closed-form iterative analytic approximation to a class of nonlinear singularly perturbed parabolic partial differential equation is developed and analysed for convergence. We have considered both parabolic reaction diffusion and parabolic convection diffusion type of problems in this paper. The solution of this class of problem is polluted by a small dissipative parameter, due to which solution often shows boundary and interior layers. A sequence of approximate analytic solution for the above class of problems is constructed using Lagrange multiplier approach. Within a general frame work, the Lagrange multiplier is optimally obtained using variational theory and Liouville-Green’s transformation. The sequence of approximate analytic solutions so obtained is proved to converge the exact solution of the problem. To demonstrate the proposed method’s efficiency and accuracy, two linear and one nonlinear test problem have been taken into account.

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A variational iteration method (VIM) for nonlinear dynamic response of a cracked plate interacting with a fluid media

Cited by 15 publications

References 54 publications

Estimating Fixed Points via New Iterative Scheme with an Application

Estimating Fixed Points via New Iterative Scheme with an Application

Variational iteration method along with intelligent computing system for the radiated flow of electrically conductive viscous fluid through porous medium

An Iterative Analytic Approximation for a Class of Non-Linear Singularly Perturbed Parabolic Partial

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