Title :
Interval Tools for ODEs and DAEs
Author_Institution :
McMaster Univ., Hamilton
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;
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
DOI :
10.1109/SCAN.2006.28
