Re: Solution of PDEs with guaranteed accuracy

Please look at the applications of interval arithmetic.

This is the main web page:
http://www.cs.utep.edu/interval-comp/main.html

Some interesting software:

COSY.(http://cosy.pa.msu.edu/)
This software package is based on Taylor model and interval methods. It
is intended for validated solution of such problems as ordinary
differential equations, quadrature, range bounding, etc. It can either
be used as a stand-alone program or via C++ and Fortran 90/95
frontends.

FADBAD/TADIFF (http://www.imm.dtu.dk/fadbad.html),
an automatic differentiation package, with applications to validated
solution of ordinary differential equations.

Other software:
http://www.cs.utep.edu/interval-comp/intsoft.html

There are also some special algorithms.
Look for example at prof. Muhanna's papers:

http://www.gtrep.gatech.edu/cee/faculty/muhanna.html

http://www.gtsav.gatech.edu/rec/recworkshop/proceedings/proceedings.html

This paper is also interesting:

NEDIALKO S. NEDIALKOV
AN INTERVAL METHOD FOR INITIAL VALUE PROBLEMS IN
LINEAR ORDINARY DIFFERENTIAL EQUATIONS
http://www.cas.mcmaster.ca/~nedialk/PAPERS/LINEAR/linear.pdf

Regards,

Andrzej Pownuk
http://andrzej.pownuk.com

.

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