Abstract: In this paper, a class of K-block implicit hybrid methods with higher order derivative for the numerical integration of initial value problems in ordinary differential equations are derived. By the methods, a block of K new values can be obtained simultaneously on S-processors. It is shown that the method of order (l + 1) (d + 1) exist, where K=s· d. The theorems of convergence and numerical stability are presented, and one numerical experiment is also given.

Key words: Ordinary differential equation, Block methods, Parallel algorithm