Abstract: 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.

Key words: ordinary differential equations, θ-block predictor-corrector methods, stability, convergence