Purely analytic approximate solutions for steady three-dimensional problem of condensation film on inclined rotating disk by homotopy analysis method

A novel analytical solution of mixed convection about an inclined flat plate embedded in a porous medium using the DTM-Padé

“…The order of padé approximation ½L; M, [8,8] has sufficient accuracy; on the other hand, if the order of padé approximation increases, the accuracy of the solution increases. So, the [8,8] Padé approximants of (20) and (21) …”

A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field

“…Furthermore, the HAM is rather general and contains the Homotopy Perturbation Method (HPM) [21], the Adomian Decomposition Method (ADM) [23] and the δ−expansion method. In recent years the HAM has been successfully employed to solve many types of non-linear problems such as the non-linear equations arising in heat transfer [24], the non-linear model of diffusion and reaction in porous catalysts [25], the chaotic dynamical systems [26], the nonhomogeneous Blasius problem [27], the generalized threedimensional MHD flow over a porous stretching sheet [28], the wire coating analysis using MHD Oldroyd 8-constant fluid [29], the axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet [30], the MHD flow of a second grade fluid in a porous channel [31], the generalized Couette flow [32], the Glauert-jet problem [33], the Burger and regularized long wave equations [34], the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field [35], the nano boundary layer flows [36], the two-dimensional steady slip flow in microchannels [37], the steady three-dimensional problem of condensation film on an inclined rotating disk [38], the generalized Benjamin-Bona-Mahony equation [39], the fifth-order Korteweg-de Vries equation [40], the boundary layer equations of power-law fluids of second grade [41] and many other problems. All of these successful applications verified the validity, effectiveness and flexibility of the HAM.…”

Loop soliton solutions of a short wave model for a degasperis-procesi equation

“…Liao (Liao SJ, 1992) employed the basic ideas of the homotopy in topology to propose method for nonlinear problems, namely homotopy analysis method (HAM) (Liao, 2010;Liao and Campo, 2002;Liao, 2003a;Liao, 2003b). This method has been successfully applied to solving many types of nonlinear problems (Molabahrami and Khania, 2009;Sajid and Hayat, 2008;Rashidi and Dinarvand, 2009;Dinarvand and Rashidi, 2010).…”