In real-time simulation of power electronic system, the modeling method and numerical integration method are key factors affecting simulation performance. The LC binary method significantly reduces hardware resource utilization and FPGA workload. However, different integration methods have varying error accuracy and convergence. This paper provides a detailed analysis of the impact of different numerical integration methods on the system and proposes an effective and versatile real-time simulation method for multi-switch circuit, demonstrated through the application case of a single-phase inverter based on LC filtering. Comparative tests with Simulink model under a real-time simulation step size of 1μs show that the proposed method achieves a relative error of less than ± 1% and consumes hardware resources by no more than 30%. This approach demonstrates practical value for efficient real-time simulation of multi-switch power electronic system.