Application of Homotopy analysis method to fourth-order parabolic partial differential equations

In this paper, by means of the homotopy analysis method (HAM), the solutions of some fourthorder parabolic partial differential equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter h that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple

Analytical solution for nonlinear Gas Dynamic equation by Homotopy Analysis Method

In this paper, the Homotopy Analysis Method (HAM) is used to implement the homogeneous gas dynamic equation. The analytical solution of this equation is calculated in form of a series with easily computable components

Analytical solution of BVPs for fourth-order integrodifferential equations by using homotopy analysis method

Abstract:An analytic technique, the homotopy analysis method (HAM), is applied to obtain the approximate analytical solutions of fourth-order integro-differential equations. The homotopy analysis method (HAM) is one of the most effective method to obtain the exact and approximate solution and provides us with a new way to obtain series solutions of such problems. HAM contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region of series solution. It is shown that the solutions obtained by the Adomian decomposition method (ADM) and the homotopy-perturbation method (HPM) are only special cases of the HAM solutions. we have shown that fourth-order boundary value problems can be transformed into a system of differential equations and integro-differential equation, which can be solved by using homotopy analysis method. Several examples are given to illustrate the efficiency and implementation of the method

GMRES implementations and residual smoothing techniques for solving ill-posed linear systems

AbstractThere are verities of useful Krylov subspace methods to solve nonsymmetric linear system of equations. GMRES is one of the best Krylov solvers with several different variants to solve large sparse linear systems. Any GMRES implementation has some advantages. As the solution of ill-posed problems are important. In this paper, some GMRES variants are discussed and applied to solve these kinds of problems. Residual smoothing techniques are efficient ways to accelerate the convergence speed of some iterative methods like CG variants. At the end of this paper, some residual smoothing techniques are applied for different GMRES methods to test the influence of these techniques on GMRES implementations

Study of Convergence of HAM and its Application on the Fokker-Planck Equation

. In this paper we prove the convergence of homotopy analysis method (HAM) and present the application of the homotopy analysis method to obtain the exact analytical solution of the Fokker-Planck equation. In the current paper this scheme will be investigated in details and efficiency of the approach will be shown by applying the procedure on several interesting and important example

SOLVING NONLINEAR KLEIN-GORDON EQUATION WITH A QUADRATIC NONLINEAR TERM USING HOMOTOPY ANALYSIS METHOD

In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple

SOLVING NONLINEAR KLEIN-GORDON EQUATION WITH A QUADRATIC NONLINEAR TERM USING HOMOTOPY ANALYSIS METHOD

In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple

Iranian Journal of Optimization Solving Nonlinear Klein-Gordon Equation with a Quadratic Nonlinear term using Homotopy Analysis Method Archive of SID www.SID.ir

Abstract In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM). Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple

A survey of four years intrauterine insemination at Shariati Hospital

Intrauterine insemination (IUI) has been practiced since the late 1800's primarily for idiopathic infertility, and in men with deficient semen parameters. The procedure is done by placing washed sperm in uterus a few hours before ovulation. The records of 427 couples receiving IUI for treatment of infertility at Shariati hospital in 1370-74 were reviewed retrospectively. These patients had IUI in 574 cycles. Eighty patients became pregnant and delivery rate was 14% per cycle. Pregnancy rate is impressive when ovulation induction is combined with insemination timed just before ovulation. The success rate in Shariati hospital is comparable to other infertility centers in the world and cost of a cycle of IUI with HMG superovulation is approximately one third the cost of IVF-ET or GIFT cycle and avoids invasive oocyte retrieval and extracorporeal fertilization. So we suggest that women with refractory infertility without anatomic distortion of pelvis can have at least 3-6 cycles of IUI before IVF or GIFT