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)
Matus, Piotr; Kozera, Ryszard; Paradzinska, Agnieszka; and Schadinskii, Denis
"Discrete Analogs of the Comparison Theorem and Two-Sided Estimates of Solution of Parabolic Equations,"
Applied Mathematics & Information Sciences: Vol. 10
, Article 8.
Available at: https://dc.naturalspublishing.com/amis/vol10/iss1/8