Simulating a physical system in real-time is widely used in equipment design, test, and validation. Though an implicit multistep numerical method excels at solving physical models that are usually composed of stiff ordinary differential equations, it is not suitable for real-time simulation because of state discontinuity and massive iterations for root finding. Thus, a method based on the backward differential formula is presented. It divides the main fixed step of real-time simulation into limited minor steps according to computing cost and accuracy demand. By analyzing and testing its capability, this method shows advantage and efficiency in real-time simulation, especially when the system contains stiff equations. A simulation application will have more flexibility while using this method.

实时仿真物理系统广泛用于设备设计、测试和验证。虽然隐式多步数值方法擅长求解通常由刚性常微分方程组成的物理模型，但由于状态不连续和求根迭代大量迭代，它不适合实时仿真。因此，提出了一种基于后向微分公式的方法。它根据计算成本和精度需求将实时仿真的主要固定步骤划分为有限的小步骤。通过分析和测试其能力，该方法在实时仿真中显示出优势和效率，特别是当系统包含刚性方程时。使用此方法时，模拟应用程序将具有更大的灵活性。