We propose and numerically demonstrate an ultrafast real-time ordinary differential equation (ODE) computing unit in optical field based on a silicon microring resonator, operating in the critical coupling region as an optical temporal differentiator. As basic building blocks of a signal processing system, a subtractor and a splitter are included in the proposed structure. This scheme is featured with high speed, compact size and integration on a siliconon- insulator (SOI) wafer. The size of this computing unit is only 35 μm × 45 μm. In this paper, the performance of the proposed structure is theoretically studied and analyzed by numerical simulations.