An Efficient Seven-point Hybrid Block Method for the Direct Solution of y''=f(x,y,y')

A Self starting Stomer Cowell Hybrid Block Method of uniform Order 8 for Direct solution of General Second Order Initial Value Problems of Ordinary Differential Equations is presented in this paper. The method produces simultaneous approximation of the solution in a Block of Seven points at x=x(n+j) j=1,2,3,4,13/3,9/2 and 14/3 at once. The Block Analysis of this method shows that it is Zero stable and convergent. Numerical experiments show there superiority over the existing method.