Abstract
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.
Highlights
Introduction distributed under the terms andSignificant interest has been paid to the analysis of nonlinear challenges in different fields of nature and engineering
Six analytical methods and two numerical techniques are applied to work out the boundary value challenge
Dinarvand and Rashidi [26] studied this problem by the homotopy asymptotic method (HAM)
Summary
Employing the differential conversion from Equation (17), the following form of equation is obtained:. − Re(k + 1 − r )(k + 2 − r )(r + 1) F (r + 1) F (k + 2 − r )} = 0 where F(k) denotes the differential transforms of n f (y) and it is defined as m. Employing Equation (22) for Equation (20) and by the recurrent technique, all magnitudes of F(k) are calculated. Equation (21), the series of solutions is defined as below:. By applying the boundary conditions of Equation (19), the constants a and b are calculated. For Re = 1 and α = 1, the values and the solutions are as follows:.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
