Abstract: In this paper, self-starting block hybrid method of
order (5,5,5,5)T is proposed for the solution of the special second
order ordinary differential equations with associated initial or
boundary conditions. The continuous hybrid formulations enable us
to differentiate and evaluate at some grids and off – grid points to
obtain four discrete schemes, which were used in block form for
parallel or sequential solutions of the problems. The computational
burden and computer time wastage involved in the usual reduction of
second order problem into system of first order equations are avoided
by this approach. Furthermore, a stability analysis and efficiency of
the block method are tested on stiff ordinary differential equations,
and the results obtained compared favorably with the exact solution.