以仅有两个互异正特征值的单构矩阵为系数的一类单块法

1．引言众所周知，解刚性常微分方程组初值问题的单块法具有良好的并行性，这里，是Kronecker乘符，为单位矩阵，Yn构造出多种A一稳定或L一稳定的r点r阶，r＋1阶，甚至r＋2阶的单块法［1－5］．但一般而言，当用Newton（型）法解（1．幻时，需对形如的矩阵做多次LU分解，当mr较大时，计算量相当巨大．为克服这一缺点，许多作者进行了努力［‘，‘，＼特别是［6］中提出的。点r阶A一稳定或L一稳定的经济隐式单块法（EIBM）X＋1＝X＋h（BO兄＊q凡十1），q21／2，（1．4）当精度要求不太高，且右函数f的计值工作量与m阶矩阵的LU分解工…

A CLASS OF ONE-BLOCK IMPLICIT METHODS WITH NONDEROGATORY COEFFICENT MATRIX HAVING ONLY TWO DIFFERENT POSITIVE EIGENVALUES

This paper presents a class of r-point r+1 order A-stable implicit one-block methods with nonderogatory coefficent matrix having only two different positive eigenvalues (abbreviated term TIBM), and a Newton-like iterative method for solving nonlinear equation system produced from the TIBM. The paper proposes also a implementation strategy (TIBMS) with variable stepsize and variable method by means of combination TIBM with EIBM (Economical Implicit Single-Block Methods). Theoretical analysis and numerical test indicate that this strategy will be hopeful for solving initial-value problems of Stiff ODEs on parallel computer.