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Approximation of solutions to multidimensional parabolic equations by approximate approximations
Sapienza University of Rome, Italy.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. University of Liverpool, England.
Weierstrass Institute Appl Anal and Stochast, Germany.
2016 (English)In: Applied and Computational Harmonic Analysis, ISSN 1063-5203, E-ISSN 1096-603X, Vol. 41, no 3, 749-767 p.Article in journal (Refereed) Published
Abstract [en]

We propose a fast method for high order approximations of the solution of n-dimensional parabolic problems over hyper-rectangular domains in the framework of the method of approximate approximations. This approach, combined with separated representations, makes our method effective also in very high dimensions. We report on numerical results illustrating that our formulas are accurate and provide the predicted approximation rate 6 also in high dimensions. (C) 2015 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2016. Vol. 41, no 3, 749-767 p.
Keyword [en]
Higher dimensions; Parabolic equation; Heat potential; Separated representations; Tensor product approximation
National Category
Mathematical Analysis
URN: urn:nbn:se:liu:diva-132040DOI: 10.1016/j.acha.2015.06.001ISI: 000384038800004OAI: diva2:1038581
Available from: 2016-10-19 Created: 2016-10-17 Last updated: 2016-10-19

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Mazya, Vladimir
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Mathematics and Applied MathematicsFaculty of Science & Engineering
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