Abstract

This research work deals with numerical quenching for a system of heat equations under nonlinear coupled boundary conditions. This problem models a heat transfer through two different materials. We obtain some conditions under which the solution of a semi-discrete form of the continuous problem quenches in finite time and estimate its semi-discrete quenching time. We also prove that the semi-discrete quenching time converges to real one, when the mesh size tends to zero. From fully discretized schemes, we have developed algorithms that have allowed us to obtain good approximations of the quenching time and other numerical results to illustrate our analysis.

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