Stability of Two-Step Methods for Variable Integration Steps

摘要

Two of the most commonly used methods, the Trapezoidal Rule and the two-step backward differentiation formula, both have drawbacks when applied to difficult stiff problems. The Trapezoidal Rule does not sufficiently damp the stiff components and the backward differentiation method is unstable for rapidly varying steps. In this paper we show that there exists a one-parameter family of two-steps, second-order one-leg methods which are stable for any test problem, using arbitrary step sequences. (Author)