Discrete Analogs of the Comparison Theorem and Two-Sided Estimates of Solution of Parabolic Equations

Authors

Piotr Matus, Institute of Mathematics, NAS of Belarus, 11 Surganov St., 220072 Minsk, Belarus\\ Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Al. Racławickie 14, 20-950 Lublin, PolandFollow
Ryszard Kozera, Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Al. Racławickie 14, 20-950 Lublin, Poland\\ Faculty of Applied Informatics and Mathematics, Warsaw University of Life Sciences - SGGW , Nowoursynowska 159, 02-776 Warsaw, PolandFollow
Agnieszka Paradzinska, Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Al. Racławickie 14, 20-950 Lublin, PolandFollow
Denis Schadinskii, Institute of Mathematics, NAS of Belarus, 11 Surganov St., 220072 Minsk, BelarusFollow

Author Country (or Countries)

Poland

Abstract

In this paper, we prove the difference analogs of the comparison theorems for solutions of the Cauchy problem for a nonlinear ordinary differential equation (ODE). These theorems are used to analyse blow-up solution of finite-difference schemes (FDS) approximating the Neumann problem for a parabolic equation with a nonlinear source of power form. We also propose the method for obtaining the two-sided estimates of solution. This method is based on implicit and explicit FDS.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100108

Recommended Citation

Matus, Piotr; Kozera, Ryszard; Paradzinska, Agnieszka; and Schadinskii, Denis (2016) "Discrete Analogs of the Comparison Theorem and Two-Sided Estimates of Solution of Parabolic Equations," Applied Mathematics & Information Sciences: Vol. 10: Iss. 1, Article 8.
DOI: http://dx.doi.org/10.18576/amis/100108
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss1/8