An efficient iterative method for solving Bratu-type equations

In this paper, an efficient analytical iterative method is introduced for solving the initial value and boundary value Bratu problems. A quasilinearization method with an optimal parameter is derived and utilized to reduce the highly nonlinear Bratu equations to a sequence of linear problems. An optimal Picard iteration method is used to obtain approximate analytical solution of linearized versions of Bratu's equations. The numerical results presented the effectiveness and high performance of the proposed method and comparisons are made with many other existing numerical solution techniques. The comparisons reveal the efficiency and applicability of the present work. (C) 2019 Elsevier B.V. All rights reserved.