Year: 2016
Author: Igor Boglaev
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 3 : pp. 262–284
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1512-m2015-0241
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 3 : pp. 262–284
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Nonlinear integro-parabolic equations of Fredholm type Nonlinear difference schemes Monotone iterative methods The method of upper and lower solutions.
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