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 and in the stability functions are given. Furthermore, we prove . With the aid of symbolic computations and the expressions of diagonal Pade' 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)