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 The finite-time blow-up phenomenon for the semilinear heat equation was widely considered since 1960's both mathematically and numerically. In this paper, we would like to consider the computation of blow-up solutions for a coupled semilinear heat equations. To this end, we study the numerical solutions for an ODE system as a first step. We propose a scheme for the computation of the numerical blow-up time and prove the convergence for the numerical solution and the numerical blow-up time. Then we apply the idea to a semilinear parabolic system whose solution may blow up in a finite time. Several numerical examples are reported and discussed.
 Abstract iContents iiList of Figures iii1 Introduction 12 A nonlinear ODE system 33 A finite difference scheme for (4) 104 Conclusion 17
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