On interval predictor-corrector methods

One can approximate numerically the solution of the initial value problem using single or multistep methods. Linear multistep methods are used very often, especially combinations of explicit and implicit methods. In floating-point arithmetic from an explicit method (a predictor), we can get the first approximation to the solution obtained from an implicit method (a corrector). We can do the same with interval multistep methods. Realizing such interval methods in floating-point interval arithmetic, we compute solutions in the form of intervals which contain all possible errors. In this paper, we propose interval predictor-corrector methods based on conventional Adams-Bashforth-Moulton and Nyström-Milne-Simpson methods. In numerical examples, these methods are compared with interval methods of Runge-Kutta type and methods based on high-order Taylor series. It appears that the presented methods yield comparable approximations to the solutions.

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