RELIABILITY IN CONCURRENT SCIENTIFIC COMPUTING FOR VOLTERRA TYPE EQUATIONS | Zendy

Hans-Jürgen Dobner | Zendy

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RELIABILITY IN CONCURRENT SCIENTIFIC COMPUTING FOR VOLTERRA TYPE EQUATIONS

Author(s) -

Hans-Jürgen Dobner

Publication year - 1999

Publication title -

bulletin of informatics and cybernetics

Language(s) - English

Resource type - Journals

eISSN - 2435-743X

pISSN - 0286-522X

DOI - 10.5109/13476

Subject(s) - reliability (semiconductor) , computer science , type (biology) , reliability engineering , mathematics , parallel computing , physics , engineering , ecology , power (physics) , quantum mechanics , biology

We deal with an efficient approach for the complete error control in scientific computing. For results obtained by standard numerical rou tines 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 poste riori error bounds for numerical approximations. This method has been applied successfully to various problems.

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