Numerical Solution of a parabolic system with blowup of the solution

TL;DR

This paper develops a numerical method for solving a parabolic system with potential finite-time blowup, providing estimates for blowup time and demonstrating convergence under certain conditions.

Contribution

It introduces a numerical scheme for a nonlinear heat conduction system with blowup behavior and proves its convergence and blowup time estimates.

Findings

Numerical solutions can blow up in finite time similar to the continuous system.

An estimate for the blowup time of the numerical solution is derived.

Convergence of the scheme is established for specific parameter values.

Abstract

In this paper, the author proposes a numerical method to solve a parabolic system of two quasilinear equations of nonlinear heat conduction with sources. The solution of this system may blow up in finite time. It is proved that the numerical solution also may blow up in finite time and an estimate of this time is obtained. The convergence of the scheme is obtained for particular values of the parameters.