Optimal homotopy analysis and control of error for implicitly defined fully nonlinear differential equations

Gorder, Robert A. Van

doi:10.1007/s11075-018-0540-0

Cited by 21 publications

(25 citation statements)

References 40 publications

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“…The optimal parameter of the known method by Liao (2010) was investigated [15]. It was utilized a variety of methods to calculate this ℎ parameter [7,10,18,23,[27][28][29].…”

Section: Optimal Homotopy Analysis Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Zaman-Kesirli Mertebeden Burgers Denklemi İçin Optimal Bir Parametre ile Homotopi Analiz Yönteminin Geliştirilmesi

ALKAN

2022

Karamanoğlu Mehmetbey Üniversitesi Mühendislik Ve Doğa Bilimleri Dergisi

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The aim of the study is to reduce the absolute error by determining the optimal value of this arbitrary parameter using the residual error function related to the selection of the arbitrary parameter h. Some numerical examples are solved and compared to existing results. The homotopy analysis method has been successfully implemented to Burgers equation to obtain serial solutions. On the base of the solutions obtained for the required equations, it has been shown that this method is applicable to time-fractional partial differential equations.

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“…The optimal parameter of the known method by Liao (2010) was investigated [15]. It was utilized a variety of methods to calculate this ℎ parameter [7,10,18,23,[27][28][29].…”

Section: Optimal Homotopy Analysis Methodsmentioning

confidence: 99%

“…Odibat (2018) proposed a new approach for the optimal choice of linear operator and initial approach [20]. Van Gorder (2019) developed a novel method for OHAM and error control for nonlinear ordinary differential equations (ODEs) [29].…”

Section: Introductionmentioning

confidence: 99%

Zaman-Kesirli Mertebeden Burgers Denklemi İçin Optimal Bir Parametre ile Homotopi Analiz Yönteminin Geliştirilmesi

ALKAN

2022

Karamanoğlu Mehmetbey Üniversitesi Mühendislik Ve Doğa Bilimleri Dergisi

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“…The present study makes use of OHAM a semi-analytical technique to solve the system of coupled nonlinear ODEs Equations (14)–(16) when subjected to the boundary conditions Equation (17) (for details see, Liao, 40 Fan and You, 41 Van-Gorder. 42 ) This technique is based on the generalized principle of Homotopy in topology to create a concurrent system for nonlinear equations. The method of OHAM offers excellent liberty to select the complementary linear operators, initial guesses, as well as base features of the problem.…”

Section: Semi-analytical Methods (Oham)mentioning

confidence: 99%

“…With appliances of appropriate variables, the non-dimensional set of flow equations are assessed. The numerical simulations have been employed with the employment of semi-analytical methods recognized as optimal homotopic analytical methodology (OHAM) (see, for details, Liao, 40 Fan and You, 41 and Van-Gorder 42 ). The nanoparticle, temperature, and also rate concentration circulations have been presented in tables and graphs.…”

Section: Introductionmentioning

confidence: 99%

Impact of surface temperature and convective boundary conditions on a Nanofluid flow over a radially stretched Riga plate

Prasad

Vaidya

Mebarek‐Oudina

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part E:

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The current work provides the optimal homotopic analytical methodology for the steady circulation over a non-isothermal radially stretched Riga plate/disc unit. The attributes of the heat, along with the mass transfer process, are assessed in the existence of variable transport and magnetic features. Radial stretched Riga disc is considered along with additional realistic boundary heating conditions, namely, prescribed surface temperature as well as prescribed surface concentration, convective boundary conditions and also zero mass flux concentration on the surface area of the Riga disc. The model tracks Brownian motion as well as the thermal diffusion of nanoparticles in fluid circulation all at once. Regulating equations, which are highly coupled, are changed right into non-dimensional equations using appropriate transformations of similarity. Through assembling series solutions, the resulting framework is planned and examined. Graphic summaries are offered for the rheological qualities of various parameters in size for velocity, temperature, as well as nanoparticles. The modified Hartman number improves the velocity distribution and reduces the temperature distribution in both prescribed surface temperature and convective boundary condition cases. The effect of the chemical reaction parameter shows the reduced concentration distribution for the prescribed surface temperature case. In contrast, it is precisely the opposite in the convective boundary condition case.

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“…The physical impacts of the governing PDEs are converted into a set of ODEs with appropriate similarity transformations. In the present work, a semi-analytical method known as Optimal Homotopy Analysis Method (OHAM) (see Liao [40], Fan and You [41], Prasad et al [42], Van Gorder [43]) has been used for solving the solutions of coupled nonlinear differential equations. The physical behavior of all the governing terms that arise in the flow problems is presented through graphs and tables.…”

Section: Introductionmentioning

confidence: 99%

Mixed convective Williamson nanofluid flow over a rotating disk with zero mass flux

et al. 2022

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This analysis concentrates on mixed convective unsteady two-dimensional, viscous hydro-magnetic Williamson nanofluid flow with heat, and mass transport toward a stretchable rotating disk with suction/injection and joule heating. In addition, convective and zero mass flux conditions are implemented at the boundary to study the flow characteristics. The converted coupled nonlinear ordinary differential equations (ODEs) are tackled utilizing a semi-analytical technique known as Optimal Homotopy Analysis Method (OHAM). The obtained outcomes are illustrated graphically to anticipate the features of the governing terms affecting the flow model. The surface skin friction, heat, and mass transport rates are deduced and discussed in detail. The validation of the present article is verified and converges to earlier published statistics. Interestingly, analysis reveals that suction/injection parameter on axial and radial velocity profiles are quite the opposite and is identical in the case of thermal and concentration buoyancy parameter. Furthermore, the Weissenberg number dominates the flow movement; the unsteady parameter lessens the momentum and thermal boundary layer (BL) thickness.

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Optimal homotopy analysis and control of error for implicitly defined fully nonlinear differential equations

Cited by 21 publications

References 40 publications

Zaman-Kesirli Mertebeden Burgers Denklemi İçin Optimal Bir Parametre ile Homotopi Analiz Yönteminin Geliştirilmesi

Zaman-Kesirli Mertebeden Burgers Denklemi İçin Optimal Bir Parametre ile Homotopi Analiz Yönteminin Geliştirilmesi

Impact of surface temperature and convective boundary conditions on a Nanofluid flow over a radially stretched Riga plate

Mixed convective Williamson nanofluid flow over a rotating disk with zero mass flux

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