In this research, a six-order, fully implicit Block Backward Differentiation Formula with two off-step points (BBDFO(6)), for the integration of first-order ordinary differential equations (ODEs) that exhibit stiffness, is proposed. The order, consistency and stability properties of the method are discussed, and the method is found to be zero stable and consistent. Hence, the method is convergent. The numerical comparisons with the existing methods of a similar type are given to demonstrate the accuracy of the derived method.

中文翻译：

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使用六阶分块向后微分公式对刚性 ODE 进行积分

在这项研究中，提出了一个具有两个离步点的六阶全隐式块向后微分公式 (BBDFO(6))，用于对表现出刚度的一阶常微分方程 (ODE) 进行积分。讨论了该方法的阶数、一致性和稳定性性质，发现该方法为零稳定和一致。因此，该方法是收敛的。给出了与现有同类方法的数值比较，以证明导出方法的准确性。