University of Tabriz Computational Methods for Differential Equations 2345-3982 7 Issue 4 (Special Issue) 2019 08 01 Using Legendre spectral element method with Quasi-linearization method for solving Bratu's problem 580 588 9207 EN Mahmoud Lotfi Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran Amjad AliPanah Department of Applied Mathematics, University of Kurdisatn Journal Article 2019 06 26 This work presented here is the solution of the one-dimensional Bratu’s problem. The nonlinear Bratu’s problem is first linearised using the quasi-linearization method and then solved by the spectral element method. We use the Legendre polynomials for interpolation. Finally we show the results with a numerical example. https://cmde.tabrizu.ac.ir/article_9207_6ca3643e72007453764061ff4e553f35.pdf