A robust layer-resolving numerical method for a free convection problem We consider free convection near a semi-infinite vertical flat plate. This problem is singularly perturbed with perturbation parameter Gr, the Grashof number. Our aim is to find numerical approximations of the solution in a bounded domain, which does not include the leading edge of the plate, for arbitrary values of Gr, = 1 or > 1. Thus, we need to determine values of the velocity components and temperature with errors that are Gr-independent. We use the Blasius approach to reformulate the problem in terms of two coupled non-linear ordinary differential equations on a semi-- infinite interval. A novel iterative numerical method for the solution of the transformed problem is described and numerical approximations are obtained for the Blasius solution functions, their derivatives and the corresponding physical velocities and temperature. The numerical method is Gr-uniform in the sense that error bounds of the form C_p N^-p, where C_p and p are independent of the Gr, are valid for the interpolated numerical solutions. The numerical approximations are therefore of controllable accuracy.