In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

In this study, the effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel are studied analytically and numerically. The governing equations of motion and energy are simplified using a long wave length approximation. A closed form solution of the momentum equation is obtained by the homotopy perturbation method (HPM) and an exact solution of the energy ...

the current paper focuses on some analytical techniques to solve the non-linear duffing oscillator with large nonlinearity. four different methods have been applied for solution of the equation of motion; the variational iteration method, he’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. the results reveal that approximation obtained by th...

The variational iterationmethod VIM 1–4 and homotopy perturbationmethod HPM 5– 8 , proposed byHe, are powerful analytical methods for various kinds of linear and nonlinear problems. For example, the variational iteration method has been applied to autonomous ordinary differential equation 9 and delay differential equation 10 . Abdou and Soliman applied this method to Schrodinger-KDV, generalize...

the present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. the proposed scheme is based on laplace transform and new homotopy perturbation methods. the fractional derivatives are considered in caputo sense. to illustrate the ability and reliability of the method some examples are provided. the results ob...

The steady three-dimensional flow of condensation or spraying on inclined spinning disk is studied analytically. The governing nonlinear equations and their associated boundary conditions are transformed into the system of nonlinear ordinary differential equations. The series solution of the problem is obtained by utilizing the homotopy perturbation method HPM . The velocity and temperature pro...

in this paper, we consider the inhomogeneous time-fractional nonlinear fisher equation with three known boundary conditions. we first apply a modified homotopy perturbation method for translating the proposed problem to a set of linear problems. then we use the separation variables  method to solve obtained problems. in examples, we illustrate that by right choice of source term in the modified...

A solution of the governing equation representing drawdown in a horizontal confined aquifer, where groundwater flow is unsteady, was first provided by Theis and famously known as solution. This given terms an exponential integral, also called well function, for which simple reliable approximations are preferred due to their practical applications. To that end, several available literature, some...

This paper investigates the numerical solution of imprecisely defined fractional order dynamic system, subjected to an unit impulse load. A mechanical spring mass system having fractional damping of order 1/2 with fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through different types of convex normalised fuzzy sets viz. triangular,...