\(E\)-stable methods for exponentially decreasing solutions of second order initial value problems (Q1066626)

Two-step methods for second order differential equations \(y''=f(t,y)\) are proposed. These methods use approximations to the first derivative, but no formula for their computation is given. The concepts of truncation error and stability (as used in this article) are misleading: e.g. method (3.6) is claimed to have a truncation error \(O(h^ 6)\) although it reduces to the trapezoidal rule for the linear test equation. Further the presented stability analysis is based on \(y'=-\lambda y\) and not on \(y''=\lambda^ 2y\).