Time dependent nonlinear partial differential equations, like for example reaction diffusion equations, are usually solved by classical time marching schemes, like Runge-Kutta methods, or linear multi-step methods. Such equations can however have solutions which blow up in finite time, and in the blowup regime, the behavior of the solution is dominated by the non-linearity. I will show two different approaches how one can construct specialized numerical time integrators which take into account the physics of the underlying non-linear problem. I will show both theoretically and numerically that their performance can be orders of magnitude better than the performance of classical time integrators for such problems.