The renormalized Numerov algorithm is applied in solving time-independent Schr?dinger equations relevant to diatom collisions at ultralow temperature. The proprieties of Feshbach resonances in 39K-133Cs collisions are investigated as an example. It shows renormalized Numerov method can give excellent results for ultracold colliding process. In contrast to improved log derivative method, renormalized Numerov method displays a certain weakness in computational efficiency with the same condition, however, it is much stable in a big range of grid step size. Hence a new propagator is proposed by combining renormalized Numerov and logarithmic derivative methods which can save computational time rapidly with a better accuracy. This algorithm can be used to solve close-coupling Schr?dinger equations at arbitrary temperature for two-body collisions.