Application of optimal homotopy asymptotic method for Lane-Emden and Emden-Fowler initial and boundary value problems

Khan, Muhammad Asim; Ali, Norhashidah Hj. Mohd.; Ullah, Shafiq

doi:10.1063/1.5136454

Cited by 2 publications

(2 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The optimal homotopy asymptotic method (OHAM) is a new analytical procedure that was developed by Marinca et al [20]. The independence of this technique from the small parameter has resulted in the power of the OHAM in solving nonlinear differential equations [21,22]. By this technique, an effective method for managing the convergence of approximation series and adjusting convergence regions is available.…”

Section: Introductionmentioning

confidence: 99%

Semi-Analytical Solution of Two-Dimensional Viscous Flow through Expanding/Contracting Gaps with Permeable Walls

Rashidi

Sheremet

Sadri

et al. 2021

MCA

View full text Add to dashboard Cite

In this research, the analytical methods of the differential transform method (DTM), homotopy asymptotic method (HAM), optimal homotopy asymptotic method (OHAM), Adomian decomposition method (ADM), variation iteration method (VIM) and reproducing kernel Hilbert space method (RKHSM), and the numerical method of the finite difference method (FDM) for (analytical-numerical) simulation of 2D viscous flow along expanding/contracting channels with permeable borders are carried out. The solutions for analytical method are obtained in series form (and the series are convergent), while for the numerical method the solution is obtained taking into account approximation techniques of second-order accuracy. The OHAM and HAM provide an appropriate method for controlling the convergence of the discretization series and adjusting convergence domains, despite having a problem for large sizes of obtained results in series form; for instance, the size of the series solution for the DTM is very small for the same order of accuracy. It is hard to judge which method is the best and all of them have their advantages and disadvantages. For instance, applying the DTM to BVPs is difficult; however, solving BVPs with the HAM, OHAM and VIM is simple and straightforward. The extracted solutions, in comparison with the computational solutions (shooting procedure combined with a Runge–Kutta fourth-order scheme, finite difference method), demonstrate remarkable accuracy. Finally, CPU time, average error and residual error for different cases are presented in tables and figures.

show abstract

Section: Introductionmentioning

confidence: 99%

Semi-Analytical Solution of Two-Dimensional Viscous Flow through Expanding/Contracting Gaps with Permeable Walls

Rashidi

Sheremet

Sadri

et al. 2021

MCA

View full text Add to dashboard Cite

show abstract

“…Many researchers applied OHAM to study fluid flow problems [26][27][28][29]. Recently, Gossaye and Kishan [13,30,31] applied the OHAM to the problem arisen from electrical MHD non-Newtonian fluid flows over a stretching sheet, and Khan et al [32] used OHAM for Lane-Emden and Emden-Fowler initial and boundary value problems.…”

Section: Introductionmentioning

confidence: 99%

Analytic Treatment for Electrical MHD Non-Newtonian Fluid Flow over a Stretching Sheet through a Porous Medium

Adem

2020

Advances in Mathematical Physics

View full text Add to dashboard Cite

In this study, an attempt has been made to investigate the mass and heat transfer effects in a BLF through a porous medium of an electrically conducting viscoelastic fluid subject to a transverse magnetic field in the existence of an external electric field, heat source/sink, and chemical reaction. It has been considered the effects of the electric field, viscous and Joule dissipations, radiation, and internal heat generation/absorption. Closed-form solutions for the boundary layer equations of viscoelastic, second-grade, and Walters’ B ′ fluid models are considered. The method of the solution includes similarity transformation. The converted equations of thermal and mass transport are calculated using the optimal homotopy asymptotic method (OHAM). The solutions of the temperature field for both prescribed surface temperature (PST) and prescribed surface heat flux (PHF) are found. It is vital to remark that the interaction of the magnetic field is found to be counterproductive in enhancing velocity and concentration distribution, whereas the presence of chemical reaction, as well as a porous matrix with moderate values of the magnetic parameter, reduces the temperature and concentration fields at all points of the flow domain.

show abstract

Application of optimal homotopy asymptotic method for Lane-Emden and Emden-Fowler initial and boundary value problems

Cited by 2 publications

References 8 publications

Semi-Analytical Solution of Two-Dimensional Viscous Flow through Expanding/Contracting Gaps with Permeable Walls

Semi-Analytical Solution of Two-Dimensional Viscous Flow through Expanding/Contracting Gaps with Permeable Walls

Analytic Treatment for Electrical MHD Non-Newtonian Fluid Flow over a Stretching Sheet through a Porous Medium

Contact Info

Product

Resources

About