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Efficient and generic algorithm for rigorous integration forward in time of dPDEs : part I
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Except where otherwise noted, this item's license is described as Udzielam licencji. Uznanie autorstwa 3.0 Polska
Efficient and generic algorithm for rigorous integration forward in time of dPDEs : part I
Bibliographic description
| title: | Efficient and generic algorithm for rigorous integration forward in time of dPDEs : part I |
| author: | Cyranka Jacek 
|
| journal title: | Journal of Scientific Computing |
| volume: | 59 |
| issue: | 1 |
| date of publication : | 2014 |
| pages: | 28-52 |
| ISSN: |
0885-7474 |
| eISSN: |
1573-7691 |
| DOI: | |
| language: | English |
| journal language: | English |
| abstract in English: | We propose an efficient and generic algorithm for rigorous integration forward in time of partial differential equations written in the Fourier basis. By rigorous integration we mean a procedure which operates on sets and return sets which are guaranteed to contain the exact solution. The presented algorithm generates, in an efficient way, normalized derivatives which are used by the Lohner algorithm to produce a rigorous bound. The algorithm has been successfully tested on several partial differential equations (PDEs) including the Burgers equation, the Kuramoto-Sivashinsky equation, and the Swift-Hohenberg equation. The problem of rigorous integration in time of partial differential equations is a problem of large computational complexity and efficient algorithms are required to deal with PDEs on higher dimensional domains, like the Navier-Stokes equation. Technicalities regarding the various optimization techniques implemented in the software used in this paper will be reported elsewhere. |
| keywords in English: | dissipative PDE, rigorous numerics, automatic differentiation, fast fourier transform, FFT, interval arithmetic |
| affiliation: | Wydział Matematyki i Informatyki : Katedra Teorii Optymalizacji i Sterowania |
| type: | journal article |
| subtype: | academic paper |
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Except where otherwise noted, this item's license is described as Udzielam licencji. Uznanie autorstwa 3.0 Polska
Projekt „Repozytorium otwartego dostępu do dorobku naukowego i dydaktycznego UJ” współfinansowany w ramach poddziałania 2.3.1 „Cyfrowe udostępnianie zasobów nauki” Programu Operacyjnego Polska Cyfrowa z Europejskiego Funduszu Rozwoju Regionalnego i budżetu państwa na podstawie umowy o dofinansowanie nr POPC.02.03.01-00-0030/17-00
