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

The construction of s-stage explicit twoand 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 additional conditions superconvergence of order p + 1 can be achieved. Further criteria for good methods are large stability intervals and small error constants. Numerical tests of these peer methods in MATLAB and comparisons with a Runge-KuttaNyström method show the efficiency of the proposed methods.