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Volume 34, Issue 3
A Numerical Method for Solving Nonlinear Integro-Differential Equations of Fredholm Type

Igor Boglaev

DOI: 10.4208/jcm.1512-m2015-0241

J. Comp. Math., 34 (2016), pp. 262-284.

Published online: 2016-06

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  • 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.

  • Keywords

Nonlinear integro-parabolic equations of Fredholm type, Nonlinear difference schemes, Monotone iterative methods, The method of upper and lower solutions.

  • AMS Subject Headings

65M06, 65N06, 65N22, 65R20.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

i.boglaev@massey.ac.nz (Igor Boglaev)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-262, author = {Boglaev , Igor}, title = {A Numerical Method for Solving Nonlinear Integro-Differential Equations of Fredholm Type}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1512-m2015-0241}, url = {http://global-sci.org/intro/article_detail/jcm/9795.html} }
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 -

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.

Boglaev , Igor. (2016). A Numerical Method for Solving Nonlinear Integro-Differential Equations of Fredholm Type. Journal of Computational Mathematics. 34 (3). 262-284. doi:10.4208/jcm.1512-m2015-0241
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