Abstract
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\(P(\bar h)\) and\(Q(\bar h)\) in the stability functions\(\xi _k (\bar h) = P(\bar h)/Q(\bar h)\) are given. Furthermore, we prove\(P( - \bar h) = Q(\bar h)\). 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)
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Communicated by Tsai Shu-tang
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Jiao-xun, K., Yu-hua, L. The numerical stabilities of multiderivative block method. Appl Math Mech 14, 129–136 (1993). https://doi.org/10.1007/BF02453354
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DOI: https://doi.org/10.1007/BF02453354