降阶向后微分公式

ORDER REDUCTION BACKWARD DIFFEREN TIATION FORMULAS FOR STIFF DIFFERENTIAL EQUATIONS

在较全面分析向后微分公式优缺点的基础上提出了于线性多步法范围内改进向后微分公式的新方案，进而构造了降阶向后微分公式．降阶向后微分公式除误差系数略大，且需要多存贮一个函数值外，其余性能全面优于同阶的向后微分公式．

In this paper,a brief survey of backward differentiation formulas (BDF)and itsseveral modified versions is given,and then a class of order reduction backward differentiation formulas (ORBDF) is presented. Theoretical analysis and numerical experiments showthat ORBDF methods have more perfect stability propertics than the corresponding BDFmethods and preserve other advantages of BDF methods,So ORBDF seems to be the mostperfect version of BDF.