In this work, a new linear explicit singularly Pstable four-step method with algebraic order 12 is constructed, explained and presented for the numerical solution of secondorder IVPs. The advantage of the new method is its simplicity in implementation and since it is explicit, it will not require any additional predictor stages. Numerical stability and phase properties of the new method are investigated. The numerical results obtained by the new method for two known problems show its superiority in efficiency, accuracy and stability.
