Numerical Solution of a parabolic system with blowup of the solution

2009/05/18 by Marie-Noëlle Le Roux, Roux, Marie-Noëlle Le
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.0905.2862

openalex publication_date 2009/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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