ON EXPLICIT INTERVAL METHODS OF ADAMS-BASHFORTH TYPE
Małgorzata A. Jankowska, Andrzej Marciniak · Computational Methods in Science and Technology · 2002
In our previous paper [1] we have considered implicit interval multistep methods of Adams-Moulton type for solving the initial value problem.On the basis of these methods and the explicit ones introduced by Sokin [2] we wanted to construct predictor-corrector (explicit-implicit) interval methods.However, it turned out that the formulas given by Šokin are incorrect even in the simplest case.Therefore, in this paper we direct our attention to the explicit interval methods of Adams-Bashforth type and modify the formulas of Šokin.For the modified explicit interval methods it is proved, like for the implicit interval methods considered in [1], that the exact solution of the problem belongs to interval-solutions obtained by these methods.Moreover, it is shown an estimation of the widths of such interval-solutions.