STABILIZED 4TH-ORDER EXTENDED METHODS FOR THE NUMERICAL-SOLUTION OF ODES

Recently, Kondrat and Jacques [1] gave an extended two-step fourth ord er A-stable method; the reason noted for giving a two-step method is t hat a one-step method of the type is not possible. Firstly, we show th at it is possible to obtain a two-parameter family of such methods whi ch are one-step, fourth order and A-stable; and, there exists a one-pa rameter sub-family of these methods which are, in addition, L-stable. Secondly, from among the extended two-step methods, it is natural to a sk if the well-known Simpson's rule can be stabilized; we present an A -stabilized version of Simpson's rule.