We consider the dynamics of a multi-component scalar field on super-horizon scales in the context of inflationary cosmology. We present a method to solve the perturbation equations on super-horizon scales, i.e., in the long wavelength limit, by using only the knowledge of spatially homogeneous background solutions. In doing so, we clarify the relation between the perturbation equations in the l...

A. Noor et al. [7] analyze a technique by combining the variational iteration method and the homotopy perturbation method which is called the variational homotopy perturbation method (VHPM) for solving higher dimensional initial boundary value problems. In this paper, we consider the VHPM to obtain exact solution to Gas Dynamics equation.

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 paper, the Kadomtsev-Petviashvili equation is solved by using the Adomian’s decomposition method , modified Adomian’s decomposition method , variational iteration method , modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The existence and uniqueness of the solution and convergence of the proposed...

The perturbation-based nonlinearity compensation (NLC) method is considered in conjunction with a forward error correction (FEC) code that capable of detecting block errors. FEC decoding performed prior to the NLC, and NLC then only for blocks, could not be decoded correctly. total complexity thus dramatically reduced down 1% some cases w.r.t. standard, hard decision-directed decoding. Negligib...

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...

The dusty plasma system (containing nonthermally distributed inertialess electron species, warm inertial ion and positively charged stationary dust species) is considered. basic features of subsonic supersonic modified-ion-acoustic solitary shock waves formed in such a have been investigated by the reductive perturbation method. It has shown that species play new role favor formation waves. On ...

We design a wavelet optimized finite difference (WOFD) scheme for solving self-adjoint singularly perturbed boundary value problems. The method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids. Small dissipation of the solution is captured significantly using an adaptive grid. The adaptive feature is performed automatically by thresholding the wavele...

The solution methods of nonlinear differential equations are very important because most of the physical phenomena are modelled by using such kind of equations. Therefore, this work presents a rational version of homotopy perturbation method RHPM as a novel tool with high potential to find approximate solutions for nonlinear differential equations. We present two case studies; for the first exa...