in this paper, an analytical method called the parametric iteration method (pim) is presented for solving the second-order singular ivps of lane-emden type, and its local convergence is discussed. since it is often useful to have an approximate analytical solution to describe the lane-emden type equa- tions, especially for ones where the closed-form solutions do not exist at all, therefore, an ...

on the basis of a reproducing kernel space, an iterative algorithm for solving the one-dimensional linear and nonlinear schrödinger equations is presented. the analytical solution is shown in a series form in the reproducing kernel space and the approximate solution is constructed by truncating the series. the convergence of the approximate solution to the analytical solution is also proved. th...

Approximate analytical methods have been frequently used in geotechnical engineering to estimate the reliability of structures due their efficiency and simplicity. The main spirit these is using moments limit state function index. However, are strongly dependent on form function, resulting fact that sensitive functions. This study aims systematically explore how various equivalent forms functio...

This paper successfully applies the Adomian decomposition  and the modified Laplace Adomian decomposition methods to find  the approximate solution of a nonlinear fractional Volterra-Fredholm integro-differential equation. The reliability of the methods and reduction in the size of the computational work give these methods a wider applicability. Also, the behavior of the solution can be formall...

in this paper, we introduce an efficient method for solving the quadratic riccati differential equation. in this technique, combination of laplace transform and new homotopy perturbation methods (ltnhpm) are considered as an algorithm to the exact solution of the nonlinear riccati equation. unlike the previous approach for this problem, so-called nhpm, the present method, does not need the init...