Abstract: In the report, a novel recurrent neural network based on integral enhancement to solve time-varying systems of equations and inequations was proposed. Firstly, a set of non-negative relaxation variables was introduced, the time-varying inequality system was transformed into the form of a matrix equation, and a matrix differential equation about the error function was constructed; secondly, the inverse transformation of the matrix was used to derive the explicit solution of the matrix differential equation, and on which an integral enhancement term was added to improve the anti-interference ability of the solving model; lastly, the final computational simulation results validated the effectiveness and superiority of the proposed integral enhanced recurrent neural network.