A numerical scheme for the blow-up time of solutions of a system of nonlinear ordinary differential equations

Based on the method of finite differences we propose a numerical blow-up time for a system of nonlinear ordinary differential equations, such system is defined by means of some parameters. Under certain conditions, on the parameters, the system blow-up in finite time. We introduce a numerical time and prove that this converges to the exact blow-up time and an error estimate is also given.