Interval Tools for ODEs and DAEs

Author

Nedialkov, N.S.

Author_Institution

McMaster Univ., Hamilton

fYear

2006

fDate

26-29 Sept. 2006

Firstpage

4

Lastpage

4

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 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.

Keywords

differential algebraic equations; initial value problems; mathematics computing; software packages; differential algebraic equation; initial value problem; interval tool; literate programming; ordinary differential equation; software package; validated solver; Application software; Arithmetic; Differential algebraic equations; Differential equations; Finite wordlength effects; Humans; Packaging; Software packages; Software tools; Taylor series;

fLanguage

English

Publisher

ieee

Conference_Titel

Scientific Computing, Computer Arithmetic and Validated Numerics, 2006. SCAN 2006. 12th GAMM - IMACS International Symposium on

Conference_Location

Duisburg

Print_ISBN

978-0-7695-2821-2

Type

conf

DOI

10.1109/SCAN.2006.28

Filename

4402394