This paper gives a class of parallel block predictor-corrector methods with a parameter θ for solving initial value problems in ordinary differential equations. The stability and convergence on iterative processes are discussed. It is proven that the methods not only have large stability intervals but also have large convergent regions, thus they are very suitable for par allel integration of ordinary differential equations.

In this paper, a class of polynomial collocation methods with the second deriva live is derived for efficient integration of stiff systems. The methods are of one-step type, and the numerical solutions at m-point can simultaneously be obtained for each application of the formulas. It is shown that this class of methods is of order 2m+1 and the stability is analysed.