Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis method

Analytical approximate solutions for two-dimensional viscous flow through expanding or contracting gaps with permeable walls

“…The HAM always provides us with a family of solution expressions in the auxiliary parameter the convergence region and rate of each solution might be determined conveniently by the auxiliary parameter Furthermore, the HAM is rather general and contains the homotopy perturbation method (HPM) [12], the Adomian decomposition method (ADM) [14] and δ-expansion method. In recent years, the HAM has been successfully employed to solve many types of nonlinear problems such as the nonlinear equations arising in heat transfer [15], the nonlinear model of diffusion and reaction in porous catalysts [16], the chaotic dynamical systems [17], the non-homogeneous Blasius problem [18], the generalized three-dimensional MHD flow over a porous stretching sheet [19], the wire coating analysis using MHD Oldroyd 8-constant fluid [20], the axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet [21], the MHD flow of a second grade fluid in a porous channel [22], the generalized Couette flow [23], the Glauert-jet problem [24], the Burger and regularized long wave equations [25], the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field [26], the nano boundary layer flows [27], the twodimensional steady slip flow in microchannels [28], and other problems. All of these successful applications verified the validity, effectiveness and flexibility of the HAM.…”

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.…”

Heat Transfer and Flows of Thermal Convection in a Fluid-Saturated Rotating Porous Medium

“…Furthermore, the homotopy analysis method provides us with a family of solution series and a simple way to adjust and control the convergence region and rate of approximation series [48]. Serving as a powerful tool to deal with nonlinear equations, the homotopy analysis method has applied to many nonlinear problems in science and engineering [51,52]. Abbasbandy [53] used the homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation.…”