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

We consider the blow-up ODE problem u ̈ = u 1 + γ ( γ > 0 ) , u ( 0 ) = a 0 > 0 , u ̇ ( 0 ) = a 1 > 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.