document: Some recent advances in validated methods for IVPs for ODEs Compared to standard numerical methods for initial value problems -LRB- IVPs -RRB- for ordinary differential equations -LRB- ODEs -RRB- , validated methods -LRB- often called interval methods -RRB- for IVPs for ODEs have two important advantages : if they return a solution to a problem , then -LRB- 1 -RRB- the problem is guaranteed to have a unique solution , and -LRB- 2 -RRB- an enclosure of the true solution is produced . We present a brief overview of interval Taylor series -LRB- ITS -RRB- methods for IVPs for ODEs and discuss some recent advances in the theory of validated methods for IVPs for ODEs . In particular , we discuss an interval Hermite-Obreschkoff -LRB- IHO -RRB- scheme for computing rigorous bounds on the solution of an IVP for an ODE , the stability of ITS and IHO methods , and a new perspective on the wrapping effect , where we interpret the problem of reducing the wrapping effect as one of finding a more stable scheme for advancing the solution
doc_bio_tags: O O O O B I O O O O O O O O O O B I I O O O O B I I O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O
extractive_keyphrases: validated methods initial value problems ordinary differential equations interval methods interval taylor series wrapping effect
abstractive_keyphrases: interval hermite-obreschkoff scheme qr algorithm