TY - JOUR
ID - 70501
TI - A new family of high-order difference schemes for the solution of second order boundary value problems
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Bisheh-Niasar, M.
AU - Saadatmandi, A.
AU - Akrami-Arani, M.
AD - Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran
AD - Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
Y1 - 2018
PY - 2018
VL - 9
IS - 3
SP - 187
EP - 199
KW - Boundary value problem
KW - Finite difference methods
KW - Bratu’s problem
KW - Troesch’s problem
KW - High accuracy
DO - 10.22052/ijmc.2018.94933.1306
N2 - Many 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.
UR - https://ijmc.kashanu.ac.ir/article_70501.html
L1 - https://ijmc.kashanu.ac.ir/article_70501_1b5245ecf65dbca70f307d3ce45217ae.pdf
ER -