A longstanding problem in braneworld cosmology is quantifying the
dynamics of cosmological perturbations. This is because, unlike the
4-dimensional case, fluctuations are governed by non-separable
partial differential equations (PDEs). We have developed a fast and
accurate code to solve the relevant equations of motion, and hence
extract observational predictions from braneworld models. Here, we
briefly review braneworld scenarios, the perturbation problem, our
numerical methods, and the results we have obtained for the
Randall-Sundrum (RS) and Dvali-Gabadadze-Porrati (DGP) scenarios.