A NUMERICAL METHOD FOR SOLVING NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS OF FREDHOLM TYPE

作     者：Igor Boglaev 

作者机构：Institute of Fundamental Sciences Massey UniversityPrivate Bag 11-222 Palmerston North New Zealand 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2016年第34卷第3期

页      面：262-284页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 070102[理学-计算数学] 0701[理学-数学] 

主　　题：Nonlinear integro-parabolic equations of Fredholm type Nonlinear differenceschemes Monotone iterative methods The method of upper and lower solutions. 

摘      要：The paper deals with a numerical method for solving nonlinear integro-parabolic prob- lems 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 analy- sis 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.