TY - JOUR
T1 - A Numerical Method for Solving Nonlinear Integro-Differential Equations of Fredholm Type
AU - Boglaev , Igor
JO - Journal of Computational Mathematics
VL - 3
SP - 262
EP - 284
PY - 2016
DA - 2016/06
SN - 34
DO - http://doi.org/10.4208/jcm.1512-m2015-0241
UR - https://global-sci.org/intro/article_detail/jcm/9795.html
KW - Nonlinear integro-parabolic equations of Fredholm type, Nonlinear difference schemes, Monotone iterative methods, The method of upper and lower solutions.
AB - <p style="text-align: justify;">The paper deals with a numerical method for solving nonlinear integro-parabolic problems of Fredholm type. A monotone iterative method, based on the method of upper and lower solutions, is constructed. This iterative method yields two sequences which converge monotonically from above and below, respectively, to a solution of a nonlinear difference scheme. This monotone convergence leads to an existence-uniqueness theorem. An analysis of convergence rates of the monotone iterative method is given. Some basic techniques for construction of initial upper and lower solutions are given, and numerical experiments with two test problems are presented.</p>