一类k步k+1阶SDBDF型混杂法

A CLASS OF kSTEP, (k+1)ST ORDER HYBRID METHODS OF SDBDF

本文在ＳＤＢＤＦ方法的基础上构造了一类ｋ步ｋ＋１阶的ＳＤＢＤＦ型混杂法，讨论了该方法的稳定性质，证明了ｋ＝１，２，３时，方法是Ａ稳定的，ｋ＝４～１０时方法是ｓｔｉｆ稳定的，同ＢＤＦ型和Ａｄａｍｓ型混杂法相比，该方法的ｓｔｉｆ稳定阶大有提高，这两类方法的ｓｔｉｆ稳定阶只能分别达到８阶和９阶〔２，３，５〕．在实现Ｎｅｗｔｏｎ迭代计算时，我们的方法要优于原ＳＤＢＤＦ方法，因此对于求解ｓｔｉｆ问题，我们的这类方法具有一定的优势。

In this paper a class of kstep, (k+1)st order hybrid methods of SDBDF is constructed and its stability properties are discussed. The methods are proved to be Astable for k=1,2,3 and stiffly stable for k=4,…,10. The stiffly stable orders of our methods are much higher than that of BDF and Adams hybrid methods of which the stiffly stable orders are up to 8 and 9 respectively. In implementation by Newton iteration, our methods are more efficient than SDBDF method for solving nonlinear stiff problems. Finally Some numerical results are presented.