General Convergence Analysis for the Perturbation Iteration Technique

Abstract

In this study, we propose a different approach of the newly developed perturbation iteration method to analyze its convergence properties when solving nonlinear equations. Our main goal is to give some theorems which prove that this technique is convergent under some special conditions. Error estimate is also provided as a result of related theorems. A few interesting problems are investigated to illustrate our arguments.

Keywords

• Perturbation iteration method,nonlinear differential equation,convergence,series expansion

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