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A fast solution method for time dependent multidimensional Schrodinger equations
Sapienza Univ, Italy.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. RUDN Univ, Russia.
Weierstrass Inst Appl Anal and Stochast, Germany.
2019 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 98, no 1-2, p. 408-429Article in journal (Refereed) Published
Abstract [en]

In this paper we propose fast solution methods for the Cauchy problem for the multidimensional Schrodinger equation. Our approach is based on the approximation of the data by the basis functions introduced in the theory of approximate approximations. We obtain high-order approximations also in higher dimensions up to a small saturation error, which is negligible in computations, and we prove error estimates in mixed Lebesgue spaces for the inhomogeneous equation. The proposed method is very efficient in high dimensions if the densities allow separated representations. We illustrate the efficiency of the procedure on different examples, up to approximation order 6 and space dimension 200.

Place, publisher, year, edition, pages
TAYLOR & FRANCIS LTD , 2019. Vol. 98, no 1-2, p. 408-429
Keywords [en]
Schrodinger equation; higher dimensions; separated representations; error estimates
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-154851DOI: 10.1080/00036811.2017.1359571ISI: 000458651400021OAI: oai:DiVA.org:liu-154851DiVA, id: diva2:1293680
Note

Funding Agencies|Ministry of Education and Science of the Russian Federation [02, a03.21.0008]

Available from: 2019-03-05 Created: 2019-03-05 Last updated: 2019-03-05

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Mazya, Vladimir
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