Abstract
Two classes of one-step methods for the solution of the ordinary initial value problem are treated. The schemes of orderm give blocks ofm approximate solutions at each step and are constructed fromm integration formulas. Since each formula is obtained by the integration of an interpolatory natural spline, it is best in the sense of Sard. Sufficient conditions for the convergence of the iterative techniques used in each block and of the discrete variable solutions are given. The notion of block stability is introduced and the regions of block stability are given for two methods. Finally, eight block methods are compared by means of some numerical data.
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