One semi-actuator stability model for rotating stall considering in-passage shock wave was developed based on a three-dimensional compressible theory

and it was evaluated to be effective by comparing the results with experiments.Winding number integral method has been developed to solve the roots of complex functions for a long time

although it is not widely used

in some way

it is more stable than Newton-Raphson iteration method.The author used this approach to solve the eigen equation of the transonic stability model

and it is strongly recommended to extend its use in other fields because of its advantages over other methods.