Interval versions for special kinds of explicit linear multistep methods

• Main Authors: Andrzej Marciniak, Malgorzata A. Jankowska
• Format: Article
• Language: English
• Published: Elsevier 2020-05-01
• Series: Results in Applied Mathematics
• Online Access: http://www.sciencedirect.com/science/article/pii/S2590037420300157

In classical theory of explicit linear multistep methods there are known special kinds of methods which have less function evaluations (in comparison to other multistep methods) and, nevertheless, they give the same accuracy (order) of the approximations obtained. In this paper for such methods we propose their interval versions. It appears that enclosures to the exact solutions obtained by these methods are better in comparison to interval versions of other multistep methods with the same number of steps. The numerical examples presented show that sometimes these enclosures are even better than those obtained by interval methods based on high-order Taylor series. Keywords: Initial value problem, Multistep methods, Explicit interval multistep methods, Floating-point interval arithmetic