Interval Tools for ODEs and DAEs
N.S. Nedialkov · 2006
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.