论文信息 - An algebraic approach toA-stable linear multistep-multiderivative integration formulas

An algebraic approach toA-stable linear multistep-multiderivative integration formulas

A general algebraic approach and some new results are given pertaining to the synthesis of linearA-stable multistep-multiderivative formulas used for integrating stiff differential equations. This problem is shown to be considerably simplified by associating to each formula a special two-variable function, termed the canonical polynomial. In particular, the canonical polynomial approach allows to solve the approximation problem in closed form and provides an easy-to-check algebraic criterion forA-stability. A lower bound is established for the maximum order of accuracy compatible withA-stability, which turns out to be identical to the absolute maximum in some particular cases. It is finally conjectured that this property holds true in general.

Y. Genin | Y. Genin

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