修改的并行多步混合方法

李寿佛,苏凯于１９９５年构造了一类用于求解刚性问题的并行混合方法（ＰＨＭ）,其计算速度与向后微分公式（ＢＤＦ）基本相同,但稳定性远优于向后微分公式．本文通过适当修改ＰＨＭ,构造了一类新的并行混合方法（ＭＰＨＭ）,新方法基本保持了ＰＨＭ的各种优势,尽管稳定域稍微减小,但方法的级阶和Ｂ相容阶都提高了一阶,数值试验表明新方法ＭＰＨＭ能够进一步改善ＰＨＭ的计算精度

MODIFIED PARALLEL MULTISTEP HYBRID METHODS

In 1995,Li Shoufu and Su Kai constructed a class of parallel multistep hybrid methods(PHM s)for solving stiff differential equations.The computing speed of these methods is almost the same as that of Backward Differentiation Formulas,whereas the stability properities of the former are considerably superior to the later.In this paper,by modifing PHM appropriately,we construct a new class of parallel hybrid methods(MPHM s).MPHM not only preserves most advantager of PHM,but also has stage order,as well as B-consistency order,one higher than that of PHM,in spite of its stability region being somewhat smaller.Numerical experiments show that MPHM improves the computing accuracy in comparison with PHM.