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...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 polynomialsP(h) and Q(h) in the stability functions h(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)展开更多
文摘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 polynomialsP(h) and Q(h) in the stability functions h(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)
