Explicit multi-step peer methods for special second-order differential equations

The construction of s-stage explicit two- and three-step peer methods of order p=2s and p=3s is considered for the solution of non-stiff second-order initial value problems where the right-hand side does not depend on y′. By numerical search with respect to large stability intervals and small error constants sequential and parallel methods are constructed. Numerical tests of these peer methods in MATLAB and comparisons with a Runge-Kutta-Nyström method show the efficiency of the proposed methods.