Stiffly stable Adams-type methods (Q1083177)

Linear combinations of Adams-Moulton correctors are constructed to find stiffly stable Adams methods. While additional previous derivatives are required to achieve orders 4, 5 and 6, the methods improve slightly upon stability angles of backward differentiation formula methods. Even though these new methods avoid the necessity of switching between formulas, some strategy is needed for detecting stiffness in a problem. This would allow switching from a predictor-corrector to a fully implicit implementation which would be needed to compensate for stiffness. The development of formulas will be quite interesting to a researcher studying new formulas. However, some typographical errors occur, and other errors may be misleading. For the Lineard-Chipant conditions only, use \(s(z)=\sum^{k}_{j=0}c_ jz^{k-j}\). Also \(S_ 0=-12A+2B\). In the first theorem on page 323, G is not sufficiently restrictive. For example, \(S_ 1\) fails if \(A=.01\), \(B=.5\), \(C=2.5\).