COMPUTATIONAL MATHEMATICS

Blow-up in difference schemes that approximate Neumann problems for nonlinear parabolic equations

D. A. Schadinskii

Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk, Belarus

Abstract: In this paper, based on the discrete analogue of comparison theorems and Jensen's inequality, blow-up conditions and upper bound of blow-up time of the solution of implicit finite-different problem which approximates Neumann problems for various nonlinear parabolic equations are obtained. Blow-up conditions and upper bound of blow-up time of approximated differential problems are given, which are obtained and based on comparison theorems and Jensen's inequality.

Keywords: comparison theorems, blow-up, discrete analogue of comparison theorems, nonlinear parabolic equations.

UDC: 519.63

Received: 23.10.2024
Revised: 02.12.2024
Accepted: 12.12.2024