Abstract. This paper concerns the study of the numerical approximation for the following initial-boundary value problem:and γ is a positive parameter. Under some assumptions, we prove that the solution of a discrete form of the above problem blows up in a finite time and estimate its numerical blow-up time. We also show that the numerical blow-up time in certain cases converges to the real one when the mesh size tends to zero. Finally, we give some numerical experiments to illustrate our analysis.

This paper concerns the study of the quenching time of the solution of the initialboundary value problem for a system of reaction-diffusion equations.

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In this paper, we study a localized nonlinear reaction diffusion equation. We investigate interactions among the localized and local sources, nonlinear diffusion with the zero boundary value condition to establish the blow-up solution and estimate the numerical approximation for the following initialboundary value problem: We find some conditions under which the solution of a discrete form of the above problem blows up in a finite time and a numerical method is proposed for estimating its numerical blow-up time. We also prove the convergence of the numerical blow-up time to the theoretical one. Finally, we give some numerical results to illustrate our analysis.

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