Improved family of block methods for special second order initial value problems [I.V.Ps].

Abstract

In this paper, efforts are directed towards generating a 2-block 3-point numerical method for solving the special second order initial value problems of the form Y\" = F(X,Y), Y(0) = Y_O, Y\'(0) = Y_OO , where Y\' is the total derivative of Y with respect to X. The scheme so developed, is an extension of Aladeselu, V.A (2006)[1], in which a 2-block 2-point scheme was developed.. The scheme is of orders 8/9, zero-stable and convergent. It is thus possible, with this scheme, to assign computational tasks at 3 points within the block to three different processors working simultaneously.

JONAMP Vol. 11 2007: pp. 153-158