Deniz, SBildik, N2024-07-182024-07-181018-36472213-686Xhttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/3708In 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. (C) 2016 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.EnglishADOMIAN DECOMPOSITION METHODHOMOTOPY ASYMPTOTIC METHODCOLLOCATION METHODEQUATIONSArticle