On the convergence of numerical blow-up time for a second order nonlinear ordinary differential equation

We consider the blow-up ODE problem ü=u1+γ(γ>0),u(0)=a0>0,u̇(0)=a1>0, and a finite difference analogue, whose solution also blows up in finite time. In this paper, not only the convergence of the numerical blow-up time is proved but also the error estimate for the convergence is derived.