Optimal perturbation iteration method for Bratu-type problems

Abstract

In this paper, we introduce the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. The proposed method is illustrated by studying Bratu-type equations. Our results show that only a few terms are required to obtain an approximate solution which is more accurate and efficient than many other methods in the literature. * Corresponding author

On the Solution of KdV-Like Equations by the Optimal Perturbation Iteration Technique

“…The approximate solution of order m can be obtained after putting 01 ,, PP into the last one of the equations (12). For more detailed information about OPIM, please see [13][14][15][16][17][18][19].…”

On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation

“…The solutions of the Volterra and Fredholm type integral equations [36], ordinary differential equation and systems [37] and the solutions of ordinary fractional differential equations [38] have given by the present method. Modification of the PIA has been also introduced by Bildik and Deniz [43][44][45].…”

A Note on Stability Analysis of Taylor Collocation Method

“…There are many efficient analytical methods to solve nonlinear problems [1][2][3][4][5]. Taylor collocation method is one of them and its principle is simple: the solution of the considered differential equation is represented as a linear combination of known functions and the unknown coefficients in this representation are found by satisfying the associated conditions, and the differential equation at an appropriate number of points in the range of interest.…”