Nordsieck representation of high order predictor-corrector Obreshkov methods and their implementation

Predictor-corrector (PC) methods for the numerical solution of stiff ODEs can be extended to include the second derivative of the solution. In this paper, we consider second derivative PC methods with the three-step second derivative Adams-Bashforth as predictor and two-step second derivative Adams-Moulton as corrector which both methods have order six. Implementation of the proposed PC method is discussed by providing Nordsieck representation of the method and preparing an starting procedure, an estimate for local truncation error and a formula for changing stepsize. Efficiency and capability of the method are shown by some numerical experiments.