Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt

By Muhammad Sajid, Tasawar Hayat, Saleem Asghar. 2007

225 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Fluid Flow and Transfer Processes, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/514fc32b8ad8c30471a3e18aa073e8fd1e338cb8

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In Biomedical Engineering

In Fluid Flow and Transfer Processes

In Modeling and Simulation

Citations in the corpus

An explicit solution of the large deformation of a cantilever beam under point load at the free tip (2008, methodology): “2 and 3. Obviously, ¯ h =− 1 gives the smallest convergence region, and the convergence region increases as ¯ h changes from −1 to 0. Note that, as pointed by Sajid et al. [ 18 ] and Abbasbandy [1], results given by the so-called “homotopy perturbation method” [9] are exactly the same as those given”
Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation (2011, methodology): “Therefore, the HAM can overcome the foregoing restrictions and limitations of perturbation methods [12].”
Notes on the homotopy analysis method: Some definitions and theorems (2009, background): “Besides, the so-called ‘‘homotopy perturbation method” [67,68] (proposed in 1998) is exactly the same as the early homotopy analysis method (proposed in 1992) and is a special case of the late homotopy analysis method in case of h ¼ 1, as illustrated by Abbasbandy [44] and proved by Sajid et al. [46”
A General Approach to Obtain Series Solutions of Nonlinear Differential Equations (2007, methodology): “Furthermore, as proved by Liao [13, 27], Hayat et al. [31] and Sajid et al. [ 32 ], and pointed out by Abbasbandy [33‐35], the homotopy analysis method logically contains the so-called non-perturbation methods such as Adomian’s decomposition method [4‐9], the δ-expansion method [10, 11], Lyapunov’s ”
An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method (2007, methodology): “However, we may obtain a power series solution with a recurrence equation [14, 15] from the homotopy analysis solution.”