Showing papers on "Homotopy analysis method published in 2013"
TL;DR: In this article, the authors examined the magnetohydrodynamic flow of non-Newtonian nanofluid in a pipe and derived explicit analytical expressions for the velocity field, the temperature distribution and nano concentration.
543 citations
TL;DR: In this paper, the authors have examined the two dimensional flow of Williamson fluid model over a stretching sheet and the governing equations of pseudoplastic Williamson fluid are modelled and then simplified by using similarity transformations and boundary layer approach.
Abstract: In the present article, we have examined the two dimensional flow of Williamson fluid model over a stretching sheet. The governing equations of pseudoplastic Williamson fluid are modelled and then simplified by using similarity transformations and boundary layer approach. The reduced equations are then solved analytically with the help of homotopy analysis method. The physical features of the model are presented and discussed through graphs.
217 citations
TL;DR: An investigation for the flow and radiation heat transfer of a nanofluid over a stretching sheet with velocity slip and temperature jump in porous medium with very good agreement to validate the present results.
Abstract: In this paper, we present an investigation for the flow and radiation heat transfer of a nanofluid over a stretching sheet with velocity slip and temperature jump in porous medium. The Brownian motion and thermophoresis are taken into account according to Rosseland’s approximation. The governing coupled partial differential equations are non-dimensionalized and solved both numerically and analytically by local similarity method. The effects of involved parameters (velocity slip, temperature jump, thermal radiation, Prandtl number, Lewis number, Brownian motion, thermophoresis) on velocity, temperature and concentration profiles are presented graphically and analyzed. Moreover, the numerical results are compared with the analytical solutions obtained by Homotopy analysis method with very good agreement to validate the present results.
196 citations
TL;DR: In this article, the authors used the homotopy analysis method (HAM) to obtain approximate solution of fractional integro-differential equations (FIDEs), and the convergence of HAM is considered for this kind of equations.
Abstract: In this paper, we have used the homotopy analysis method (HAM) to obtain approximate solution of fractional integro-differential equations (FIDEs). Convergence of HAM is considered for this kind of equations. Also some examples are given to illustrate the high efficiency and precision of HAM. Keywords: Fractional integro-differential equation, homotopy analysis method, convergence control parameter Quaestiones Mathematicae 36(2013), 93–105
144 citations
TL;DR: In this paper, the accuracy of the homotopy analysis method (HAM) for solving the fractional order problem of the spread of a non-fatal disease in a population was investigated.
140 citations
TL;DR: In this article, the forced-convection boundary-layer of MHD Al2O3 water nanofluid flow over a horizontal stretching flat plate is investigated using Homotopy Analysis Method (HAM) and fourth order Runge-Kutta numerical method.
111 citations
TL;DR: In this paper, the authors investigated the theoretical study of steady stagnation point flow with heat transfer of a second grade nano fluid towards a stretching surface, where the fluid impinges on the wall obliquely.
110 citations
TL;DR: In this article, the homotopy decomposition method (HDM) was used to solve a system of fractional nonlinear differential equations that arise in the model for HIV infection of CD4+ T cells and attractor one-dimensional Keller-Segel equations.
Abstract: In this paper, we make use of the relatively new analytical technique, the homotopy decomposition method (HDM), to solve a system of fractional nonlinear differential equations that arise in the model for HIV infection of CD4+ T cells and attractor one-dimensional Keller-Segel equations. The technique is described and illustrated with a numerical example. The reliability of HDM and the reduction in computations give HDM a wider applicability. In addition, the calculations involved in HDM are very simple and straightforward.
104 citations
TL;DR: In this article, the homotopy decomposition method (HPM) was used for solving the nonlinear fractional coupled Korteweg-de-Vries equations.
Abstract: We put into practice a relatively new analytical technique, the homotopy decomposition method, for solving the nonlinear fractional coupled-Korteweg-de-Vries equations. Numerical solutions are given, and some properties exhibit reasonable dependence on the fractional-order derivatives’ values. The fractional derivatives are described in the Caputo sense. The reliability of HDM and the reduction in computations give HDM a wider applicability. In addition, the calculations involved in HDM are very simple and straightforward. It is demonstrated that HDM is a powerful and efficient tool for FPDEs. It was also demonstrated that HDM is more efficient than the adomian decomposition method (ADM), variational iteration method (VIM), homotopy analysis method (HAM), and homotopy perturbation method (HPM).
86 citations
TL;DR: In this article, the effects of thermal radiation in mixed convection stagnation point flow over a moving surface subject to convective boundary conditions is addressed and nonlinear analysis is presented through implementation of homotopy analysis method.
Abstract: Effects of thermal radiation in mixed convection stagnation point flow over a moving surface subject to convective boundary conditions is addressed. Mathematical modeling is based upon constitutive equations of an incompressible Maxwell fluid. Nonlinear analysis is presented through implementation of homotopy analysis method. Numerical values of Local Nusselt number is computed and analyzed.
80 citations
TL;DR: In this paper, a user friendly algorithm based on new homotopy perturbation Sumudu transform method (HPSTM) is proposed to solve nonlinear fractional gas dynamics equation.
Abstract: A user friendly algorithm based on new homotopy perturbation Sumudu transform method (HPSTM) is proposed to solve nonlinear fractional gas dynamics equation. The fractional derivative is considered in the Caputo sense. Further, the same problem is solved by Adomian decomposition method (ADM). The results obtained by the two methods are in agreement and hence this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of Sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The numerical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive.
TL;DR: In this paper, a modified homotopy perturbation method is proposed to solve the MHD boundary-layer equations, where the viscous fluid is electrically conducting in the presence of a uniform applied magnetic field and the induced magnetic field is neglected for small magnetic Reynolds number.
TL;DR: In this paper, the semi-numerical techniques known as the optimal homotopy analysis method (HAM) and Differential Transform Method (DTM) are applied to study the magneto-hemodynamic laminar viscous flow of a conducting physiological fluid in a semi-porous channel under a transverse magnetic field.
TL;DR: In this article, the convergence of q-homotopy analysis method (q-HAM) is studied and it is proven that under certain conditions the solution of the equation is known.
Abstract: The convergence of q- homotopy analysis method (q-HAM) is studied in the present paper. It is proven that under certain conditions the solution of the equation:
TL;DR: In this paper, a new approximate method, namely homotopy perturbation transform method (HPTM), is introduced to provide an analytical approximate solution to time-fractional Cauchy-reaction diffusion equation.
Abstract: The aim of this article is to introduce a new approximate method, namely homotopy perturbation transform method (HPTM) which is a combination of homotopy perturbation method (HPM) and Laplace transform method (LTM) to provide an analytical approximate solution to time-fractional Cauchy-reaction diffusion equation. Reaction diffusion equation is widely used as models for spatial effects in ecology, biology and engineering sciences. A good agreement between the obtained solution and some well-known results has been demonstrated. The numerical solutions obtained by proposed method indicate that the approach is easy to implement and accurate. Some numerical illustrations are given. These results reveal that the proposed method is very effective and simple to perform for engineering sciences problems.
TL;DR: In this article, the homotopy perturbation method, Sumudu transform, and He's polynomials are combined to obtain the solution of fractional Black-Scholes equation.
Abstract: The homotopy perturbation method, Sumudu transform, and He’s polynomials are combined to obtain the solution of fractional Black-Scholes equation. The fractional derivative is considered in Caputo sense. Further, the same equation is solved by homotopy Laplace transform perturbation method. The results obtained by the two methods are in agreement. The approximate analytical solution of Black-Scholes is calculated in the form of a convergence power series with easily computable components. Some illustrative examples are presented to explain the efficiency and simplicity of the proposed method.
TL;DR: In this paper, a linear relationship between the film thickness β and the unsteadiness parameter S is found and the effects of S, the solid volume fraction of the nanofluid ϕ and the Prandtl number Pr on the velocity and the temperature distributions are presented and discussed, respectively.
TL;DR: In this article, the effects of the Grashof number Gr and the Prandtl number Pr on the nanofluid flows are investigated successively, by means of a new set of similarity variables, the governing equations are reduced to a set of three coupled equations with an unknown constant.
TL;DR: In this paper, the steady boundary layer flow of a non-Newtonian fluid over a nonlinear stretching sheet is investigated and the Sisko fluid model, which is combination of power-law and Newtonian fluids in which the fluid may exhibit shear thinning/thickening behaviors, is considered.
Abstract: In this paper, the steady boundary layer flow of a non-Newtonian fluid over a nonlinear stretching sheet is investigated. The Sisko fluid model, which is combination of power-law and Newtonian fluids in which the fluid may exhibit shear thinning/thickening behaviors, is considered. The boundary layer equations are derived for the two-dimensional flow of an incompressible Sisko fluid. Similarity transformations are used to reduce the governing nonlinear equations and then solved analytically using the homotopy analysis method. In addition, closed form exact analytical solutions are provided for n = 0 and n = 1. Effects of the pertinent parameters on the boundary layer flow are shown and solutions are contrasted with the power-law fluid solutions. Keywords: Sisko fluid, boundary layer flow, non-linear stretching sheet, analytical solution Quaestiones Mathematicae 36(2013), 137–151
TL;DR: In this article, an analytical treatment of a steady boundary layer flow of an Eyring-Powell model fluid due to a stretching cylinder with temperature dependent variable viscosity is presented.
TL;DR: In this article, a uniform magnetic field is applied vertically to the flow direction and the governing equations are reduced to non-linear coupled partial differential equations and solved by means of homotopy analysis method.
Abstract: In this paper, we study the unsteady coupled heat and mass transfer of two-dimensional MHD fluid over a moving oscillatory stretching surface with Soret and Dufour effects. Viscous dissipation effects are adopted in the energy equation. A uniform magnetic field is applied vertically to the flow direction. The governing equations are reduced to non-linear coupled partial differential equations and solved by means of homotopy analysis method (HAM). The effects of some physical parameters such as magnetic parameter, Dufour number, Soret number, the Prandtl number and the ratio of the oscillation frequency of the sheet to its stretching rate on the flow and heat transfer characteristics are illustrated and analyzed.
TL;DR: In this paper, an approximated analytical solution for a dynamic model for the prevalence of the smoking habit in a constant population but with equal and different from zero birth and death rates was obtained.
Abstract: We obtain an approximated analytical solution for a dynamic model for the prevalence of the smoking habit in a constant population but with equal and different from zero birth and death rates. This model has been successfully used to explain the evolution of the smoking habit in Spain. By means of the Homotopy Analysis Method, we obtain an analytic expression in powers of time t which reproduces the correct solution for a certain range of time. To enlarge the domain of convergence we have applied the so-called optimal convergence-control parameter technique and the homotopy-Pade technique. We present and discuss graphical results for our solutions.
TL;DR: In this paper, an analytical solution for the coupled one-dimensional time fractional nonlinear shallow water system is obtained by using the homotopy perturbation method (HPM).
Abstract: In this paper, an analytical solution for the coupled one-dimensional time fractional nonlinear shallow water system is obtained by using the homotopy perturbation method (HPM). The shallow water equations are a system of partial differential equations governing fluid flow in the oceans (sometimes), coastal regions (usually), estuaries (almost always), rivers and channels (almost always). The general characteristic of shallow water flows is that the vertical dimension is much smaller than the typical horizontal scale. This method gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. A very satisfactory approximate solution of the system with accuracy of the order 10-4 is obtained by truncating the HPM solution series at level six.
TL;DR: In this article, fractional derivatives in the sense of Caputo and the homotopy analysis method are used to construct an approximate solution for the nonlinear space, and numerical results show that the approaches are easy to implement and accurate when applied to the non linear space.
Abstract: The fractional derivatives in the sense of Caputo and the homotopy analysis method are used to construct an approximate solution for the nonlinear space—time fractional derivatives Klein—Gordon equation. The numerical results show that the approaches are easy to implement and accurate when applied to the nonlinear space—time fractional derivatives Klein—Gordon equation. This method introduces a promising tool for solving many space—time fractional partial differential equations. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.
TL;DR: In this paper, the authors examined the unsteady mixed convection flow of magnetohydrodynamics (MHD) flow on a rotating cone in a rotating frame and the governing equations of motion in curvilinear coordinates system in the presence of MHD and convection are given.
Abstract: In this article, we have examined the unsteady mixed convection flow of magnetohydrodynamics (MHD) flow on a rotating cone in a rotating frame. The governing equations of motion in curvilinear coordinates system in the presence of MHD and convection are given. The highly nonlinear differential equations are reduced with the help of similarity transformations and the boundary layer approach. The solutions of reduced equations for rotating cone boundaries are established analytically with the help of homotopy analysis method. The heat transfer analysis for prescribed wall temperature and prescribed heat flux are considered. The expressions for velocity, temperature and concentration are computed and discussed through graphs for various emerging parameters.
01 May 2013
TL;DR: In this article, it was shown that the Harsanyi-Selten algorithm is PSPACE-complete to implement, as well as several other homotopy-based algorithms for finding equilibria of games.
Abstract: We show that the widely used homotopy method for solving fixpoint problems, as well as the Harsanyi-Selten equilibrium selection process for games, are PSPACE-complete to implement. Extending our result for the Harsanyi-Selten process, we show that several other homotopy-based algorithms for finding equilibria of games are also PSPACE-complete to implement. A further application of our techniques yields the result that it is PSPACE-complete to compute any of the equilibria that could be found via the classical Lemke-Howson algorithm, a complexity-theoretic strengthening of the result in Savani and von Stengel [2006]. These results show that our techniques can be widely applied and suggest that the PSPACE-completeness of implementing homotopy methods is a general principle.
TL;DR: In this article, the homotopy analysis method (HAM) and the Adomian's decomposition method (ADM) were applied for solving time-fractional Fornberg-Whitham equation.
TL;DR: The results indicate that temperature and the thermal boundary layer thickness appreciably increase when the Brownian motion and thermophoresis effects are strengthened and the nanoparticles volume fraction is found to increased when the thermophoretic effect intensifies.
Abstract: This investigation is concerned with the stagnation-point flow of nanofluid past an exponentially stretching sheet. The presence of Brownian motion and thermophoretic effects yields a coupled nonlinear boundary-value problem (BVP). Similarity transformations are invoked to reduce the partial differential equations into ordinary ones. Local similarity solutions are obtained by homotopy analysis method (HAM), which enables us to investigate the effects of parameters at a fixed location above the sheet. The numerical solutions are also derived using the built-in solver bvp4c of the software MATLAB. The results indicate that temperature and the thermal boundary layer thickness appreciably increase when the Brownian motion and thermophoresis effects are strengthened. Moreover the nanoparticles volume fraction is found to increase when the thermophoretic effect intensifies.
TL;DR: In this paper, a path-following algorithm for finding approximate zero of polynomial equations in the Turing machine model has been proposed, and the total bit complexity is linear in the length of the path in the condition metric, and polynomially in the logarithm of the maximum of the condition number along the path.
Abstract: We describe, for the first time, a completely rigorous homotopy (path-following) algorithm (in the Turing machine model) to find approximate zeros of systems of polynomial equations. If the coordinates of the input systems and the initial zero are rational our algorithm involves only rational computations, and if the homotopy is well posed an approximate zero with integer coordinates of the target system is obtained. The total bit complexity is linear in the length of the path in the condition metric, and polynomial in the logarithm of the maximum of the condition number along the path, and in the size of the input.
TL;DR: In this article, a user friendly algorithm based on new homotopy perturbation transform method (HPTM) is proposed to solve nonlinear fractional Fornberg-Whitham equation in wave breaking.