Interval Tools for ODEs and DAEs

Authors:
Affiliations:
Venue:
SCAN '06 Proceedings of the 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
Year:
2006

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Abstract

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 suc- cessor of the author's VNODE package. VNODE-LP is implemented entirely using literate programming. A ma- jor 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 solu- tions in differential algebraic equations.