The Numerical Stabilities of Multiderivative Block Method

In [1],a class of multiderivative block methods(MDBM) was studied for the numerical solutions of stiff ordinary differential equations.This paper is aimed at solving the problem proposed in [1] that what conditions should be fulfilled for MDBMs in order to guarantee the A-stabilities.The explicit expressions of the polynomials P(h) and Q(h) in the stability functions ξ^k(h)=P(h)/Q(h)are given.Furthermore,we prove P(-h)=Q(h).With the aid of symbolic computations and the expressions of diagonal Fade approximations,we obtained the biggest block size k of the A-stable MDBM for any given l(the order of the highest derivatives used in MDBM,l≥1)