Explicit two-step methods for second-order linear IVPs

We present a new type of method for the integration of systems of linear inhomogeneous initial value problems with constant coefficients. Our methods are of hybrid explicit Numerov type. The methods are constructed without the intermediate use of high accuracy interpolatory nodes, since only the Taylor expansion at the internal points is needed. Then we derive the order conditions taking advantage of the special structure of the problem considered. We present a method with algebraic order seven at a cost of only four stages per step. Numerical results over some linear problems, especially arising from the semidiscretization of the wave equation, indicate the superiority of the new method.