Journal ArticleDOI
An effective approach for approximate analytical solutions of the damped Duffing equation
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TLDR
In this paper, it is shown that the employed homotopy method yields uniformly convergent solutions, and the obtained explicit analytical expressions for the solution generate results that compare excellently with the numerically computed ones, which are further confirmed analytically by the absolute error formula.Abstract:
This paper deals with the purely analytic solutions to the damped Duffing equation. It is shown that the employed homotopy method yields uniformly convergent solutions. Optimum values of the convergence control parameter of the computed homotopy series are calculated from the square residual error. The obtained explicit analytical expressions for the solution generate results that compare excellently with the numerically computed ones, which are further confirmed analytically by the absolute error formula.read more
Citations
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An effective approach for evaluation of the optimal convergence control parameter in the homotopy analysis method
TL;DR: In this article, the authors proposed a rapid and effective way of working out the optimum convergence control parameter in the homotopy analysis method (HAM) for solving algebraic, highly nonlinear differentialdifference, integro-differential, and ordinary or partial differential equations or systems.
Journal ArticleDOI
Thermophoresis and thermal radiation with heat and mass transfer in a magnetohydrodynamic thin-film second-grade fluid of variable properties past a stretching sheet
TL;DR: In this article, the influence of thermophoresis and thermal radiation on the thermal conductivity and viscosity of a second-grade fluid with heat and mass transfer flow in the presence of viscous dissipation past a stretching sheet is analyzed.
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Stretched flow of Carreau nanofluid with convective boundary condition
TL;DR: In this article, the steady laminar boundary layer flow of Carreau nanofluid over a stretching sheet is investigated and the effects of Brownian motion and thermophoresis are present.
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Bioconvection in Second Grade Nanofluid Flow Containing Nanoparticles and Gyrotactic Microorganisms
TL;DR: In this article, the bioconvection in steady second grade nanofluid thin film flow containing nanoparticles and gyrotactic microorganisms is considered using passively controlled nano-fluid model boundary conditions.
Journal ArticleDOI
Magnetohydrodynamic second-grade nanofluid flow containing nanoparticles and gyrotactic microorganisms
TL;DR: In this article, the steady two-dimensional magnetohydrodynamic second-grade nanofluid flow containing nanoparticles and gyrotactic microorganisms is considered using passively controlled nano-fluid model boundary conditions for the biofluid, the thermal boundary layer convective boundary conditions have been handled.
References
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Journal ArticleDOI
Variational iteration method-Some recent results and new interpretations
TL;DR: The main concepts in variational iteration method, such as general Lagrange multiplier, restricted variation, correction functional, are explained heuristically and the solution procedure is systematically addressed, in particular, for nonlinear oscillators.
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Notes on the homotopy analysis method: Some definitions and theorems
TL;DR: In this article, the basic ideas and current developments of the homotopy analysis method, an analytic approach to get convergent series solutions of strongly nonlinear problems, which recently attracts interests of more and more researchers, are described.
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An optimal homotopy-analysis approach for strongly nonlinear differential equations
TL;DR: In this paper, an optimal homotopy analysis approach is described by means of the nonlinear Blasius equation as an example, which can be used to get fast convergent series solutions of different types of equations with strong nonlinearity.
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The application of homotopy analysis method to nonlinear equations arising in heat transfer
TL;DR: In this paper, the homotopy analysis method (HAM) is compared with the numerical and HPM in the heat transfer file and the auxiliary parameter ℏ, which provides a simple way to adjust and control the convergence region of solution series.
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A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate
TL;DR: In this paper, the homotopy analysis method was applied to give an analytic solution of the two-dimensional laminar viscous flow over a semi-infinite flat plate.