University of KashanIranian Journal of Mathematical Chemistry2228-64899320180901A new family of high-order difference schemes for the solution of second order boundary value problems1871997050110.22052/ijmc.2018.94933.1306ENM.Bisheh-NiasarDepartment of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, IranA.SaadatmandiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, IranM.Akrami-AraniDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, IranJournal Article20170809Many problems in chemistry, nanotechnology, biology, natural science, chemical physics and engineering are modeled by two point boundary value problems. In general, analytical solution of these problems does not exist. In this paper, we propose a new class of high-order accurate methods for solving special second order nonlinear two point boundary value problems. Local truncation errors of these methods are discussed. To illustrate the potential of the new methods, we apply them for solving some well-known problems, including Troesch’s problem, Bratu’s problem and certain singularly perturbed problem. Bratu’s problem and Troech’s problems, may be used to model some chemical reaction-diffusion and heat transfer processes. We also compare the results of this work with some existing results in the literature and show that the new methods are efficient and applicable.https://ijmc.kashanu.ac.ir/article_70501_1b5245ecf65dbca70f307d3ce45217ae.pdf