Interval Tools for ODEs and DAEs

We overview the current state of interval methods and software for computing bounds on solutions in initial value problems (IVPs)for ordinary differential equations (ODEs). We introduce the VNODE-LP solver for IVP ODEs, a successor of the author's VNODE package. VNODE-LP is implemented entirely using literate programming. A major goal of the VNODE-LP work is to produce an interval solver such that its correctness can be verified by a human expert, similar to how mathematical results are certified for correctness. We also discuss the state in computing bounds on solutions in differential algebraic equations.