改进的向后微分公式

Improved BDF for Stiff Differential Equations

采用增加方法步数的办法构造了两类求解刚性微分方程的改进的向后微分公式IBDF1及IBDF2。理论分析和数值试验表明,这两类新方法在较大地改善了BDF的稳定性的同时保持了BDF原有的主要优点。

Two classes of improved backward differentiation formulae for stiff differential equations were proposed by increasing the method＇s step number,whose abbreviations are IBDF1 and IBDF2 respectively.Theoretical analysis and numerical experiments show that these two classes of new methods preserve the original advantages of BDF with more perfect stability properties than the corresponding BDF.