RELIABILITY IN CONCURRENT SCIENTIFIC COMPUTING FOR VOLTERRA TYPE EQUATIONS - Collections

＜journal article＞
RELIABILITY IN CONCURRENT SCIENTIFIC COMPUTING FOR VOLTERRA TYPE EQUATIONS

Creator	Creator Name Dobner, Hans-Jurgen Affiliation Affiliation Name Mathematischess Institut II, Universitat Karlsruhe
Language	English
Publisher	Research Association of Statistical Sciences
Publisher	統計科学研究会
Date	1999-03
Source Title	Bulletin of informatics and cybernetics
Vol	31
Issue	1
First Page	1
Last Page	14
Publication Type	Version of Record
Access Rights	open access
Crossref DOI	https://doi.org/10.5109/13476
Related DOI	Bulletin of informatics and cybernetics \|\| 31(1) \|\| p1-14
Related DOI	http://bic.math.kyushu-u.ac.jp/
Related URI	Bulletin of informatics and cybernetics \|\| 31(1) \|\| p1-14
Related URI	http://bic.math.kyushu-u.ac.jp/
Relation	Bulletin of informatics and cybernetics \|\| 31(1) \|\| p1-14
Relation	http://bic.math.kyushu-u.ac.jp/
Abstract	We deal with an efficient approach for the complete error control in scientific computing. For results obtained by standard numerical routines we provide in an additional validation step existence and... enclosure of the corresponding solutions. The basic ideas of these methods are derived exemplary for nonlinear Volterra equations and then generalized to various initial value problems. We combine principles from functional analysis and enclosure theory to determine realistic and reliable a posteriori error bounds for numerical approximations. This method has been applied successfully to various problems.show more

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