In this paper, we present an explicit six-step singularly P-stable Obrechkoff methodof tenth algebraic order for solving second-order linear periodic and oscillatory initialvalue problems of ordinary differential equations. The advantage of this new singu-larly P-stable Obrechkoff method is that it is a high-order explicit method, and thusdoes not require additional predictor stages. The numerical stability and phase prop-erties of the new method is analyzed. Four numerical examples show that the newexplicit method is more accurate than Obrechkoff schemes of the same order whenapplied to the numerical solution of second-order initial value problems with highlyoscillatory solutions.
