P-stable Obrechkoff methods of arbitrary order for second-order differential equations

Following the ideas of Ananthakrishnaiah we develop a family of P-stable Obrechkoff methods of arbitrary even order. The coefficients of these methods follow from a recursive algorithm. It is also shown that the stability functions of the thus obtained methods can be expressed as Padé approximants of the exponential function with a complex argument. A numerical example is given to illustrate the performance of the methods.