Parallel Plate Flow of a Third-Grade Fluid and a Newtonian Fluid With Variable Viscosity

Yıldız, Volkan; Pakdemi̇rli̇, Mehmet; Aksoy, Yiğit

doi:10.1515/zna-2016-0064

Cited by 5 publications

(1 citation statement)

References 27 publications

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“…Pakdemirli (2017) showed that the method is effective for large perturbation parameters also by considering nonlinear vibration problems. Yıldız et al (2016) applied the method to Newtonian and non-Newtonian fluid problems. Deniz and Bildik (2017) studied the Lane–Emden type equations arising in astrophysics.…”

Section: Introductionmentioning

confidence: 99%

The new shift perturbation method with applications to vibrational problems

Pakdemi̇rli̇

2023

Journal of Vibration and Control

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Employing variable horizontal and vertical shifts for the unperturbed solution, a new perturbation method is proposed. The new method is named as the shift perturbation method. The existing perturbation methods are interpreted with respect to the horizontal and vertical shifts for the unperturbed solution. The new method is applied to some well-known vibrational problems. The method is capable of producing admissible approximate solutions for a wide range of problems such as the free and forced vibrations of the Duffing equation, equations with quadratic and cubic nonlinearities, variable amplitude nonlinear problems, and boundary layer problems. A variant of the method also produced valid solutions for large perturbation parameters.

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Section: Introductionmentioning

confidence: 99%

The new shift perturbation method with applications to vibrational problems

Pakdemi̇rli̇

2023

Journal of Vibration and Control

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Bionics-based design aimed at solving particulate sedimentation and engineered synthesis of large-sized energetic coated granules with improved performances

Wu,

Zhang,

Shi

et al. 2024

Journal of Materials Research and Technology

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New Numerical Iteration Schemes Based on Perturbation Iteration Algorithms

Pakdemirli

2023

Int. J. Comput. Methods

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Perturbation–Iteration algorithms (PIA) have been developed recently to solve differential equations analytically. A continuous solution in terms of closed form functions as an approximation of the original equation can be found using the method. The method has been implemented to algebraic equations, ordinary and partial differential equations successfully. Based on the formalism developed previously, in this work, purely numerical versions of the perturbation–iteration algorithms are proposed for the first time for first-order nonlinear ordinary differential equations. The new algorithms are called as the Numerical Perturbation–Iteration Algorithms (NPIA) to distinguish them from the continuous analytical ones (PIA) and the method in general will be called the Numerical Perturbation–Iteration Method (NPIM). Iteration schemes based on one correction term in the perturbation solution and first-order derivatives in the Taylor series expansions (NPIA(1,1)), and one correction term in the perturbations and second-order derivatives in the series expansions (NPIA(1,2)) are derived. The numerical results are compared with the exact solutions and a very good match is observed. NPIA(1,2) produced slightly better results compared to NPIA(1,1) with total errors being at least [Formula: see text], [Formula: see text] being the step size for both methods. An improvement suggestion for NPIA(1,1) is proposed in the last section to eliminate unrealistic blow-up solutions which are encountered for some specific equations.

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Parallel Plate Flow of a Third-Grade Fluid and a Newtonian Fluid With Variable Viscosity

Cited by 5 publications

References 27 publications

The new shift perturbation method with applications to vibrational problems

The new shift perturbation method with applications to vibrational problems

Bionics-based design aimed at solving particulate sedimentation and engineered synthesis of large-sized energetic coated granules with improved performances

New Numerical Iteration Schemes Based on Perturbation Iteration Algorithms

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