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Low-regularity and high oscillations: numerical analysis and computation of dispersive evolution equations

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

A Semi-implicit Exponential Low-Regularity Integrator for the Navier--Stokes Equations

Author(s): Buyang Li; Shu Ma; Katharina Schratz
Published in: SIAM Journal of Numerical Analysis, Issue 3, 2022, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/21m1437007

Convergence, error analysis and longtime behavior of the Scalar Auxiliary Variable method for the nonlinear Schrödinger equation

Author(s): Poulain, Alexandre; Schratz, Katharina
Published in: IMA Journal of Numerical Analysis, 2021, Issue 15, 2021, ISSN 1464-3642
Publisher: Oxford University Press
DOI: 10.1093/imanum/drab082

Uniformly accurate integrators for Klein–Gordon–Schrödinger systems from the classical to non-relativistic limit regime

Author(s): Maria Cabrera Calvo
Published in: Journal of Computational and Applied Mathematics, Issue 10, 2023, ISSN 1879-1778
Publisher: Elsevier
DOI: 10.1016/j.cam.2022.114756

A μ-mode BLAS approach for multidimensional tensor-structured problems

Author(s): Franco Zivcovich; Marco Caliari; Fabio Cassini
Published in: Numerical Algorithms, Issue 8, 2022, ISSN 1017-1398
Publisher: Baltzer Science Publishers B.V.
DOI: 10.1007/s11075-022-01399-4

Resonance based schemes for dispersive equations via decorated trees

Author(s): Bruned, Yvain; Schratz, Katharina
Published in: Forum of Mathematics, Pi, Issue 1, 2022, ISSN 2050-5086
Publisher: Cambridge University Press
DOI: 10.48550/arxiv.2005.01649

Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces

Author(s): Ostermann, Alexander; Rousset, Frédéric; Schratz, Katharina
Published in: Journal of the European Mathematical Society, Issue 6, 2022, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.48550/arxiv.2006.12785

Error estimates at low regularity of splitting schemes for NLS

Author(s): Alexander Ostermann, Frédéric Rousset, Katharina Schratz
Published in: Mathematics of Computation, 2021, Page(s) 1, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3676

Low-regularity integrators for nonlinear Dirac equations

Author(s): Katharina Schratz, Yan Wang and Xiaofei Zhao
Published in: Mathematics of Computation, 2020, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3557

Uniformly accurate low regularity integrators for the Klein--Gordon equation from the classical to non-relativistic limit regime

Author(s): María Cabrera Calvo; Katharina Schratz
Published in: SIAM Journal of Numerical Analysis, Issue 4, 2022, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.48550/arxiv.2104.11672

A second-order low-regularity correction of Lie splitting for the semilinear Klein–Gordon equation

Author(s): Buyang Li; Katharina Schratz; Franco Zivcovich
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, Issue 7, 2023, ISSN 2822-7840
Publisher: EDP sciences
DOI: 10.1051/m2an/2022096

Asymptotic preserving trigonometric integrators for the quantum Zakharov system

Author(s): Simon Baumstark, Katharina Schratz
Published in: BIT Numerical Mathematics, Issue 61/1, 2021, Page(s) 61-81, ISSN 0006-3835
Publisher: Lunds Universitet
DOI: 10.1007/s10543-020-00815-2

Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity

Author(s): Alexander Ostermann, Frédéric Rousset, Katharina Schratz
Published in: Foundations of Computational Mathematics, Issue 21/3, 2021, Page(s) 725-765, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-020-09468-7

Low regularity integrators for semilinear parabolic equations with maximum bound principles

Author(s): Cao-Kha Doan, Thi-Thao-Phuong Hoang, Lili Ju, Katharina Schratz
Published in: BIT Numerical Mathematics, 2023, ISSN 0006-3835
Publisher: Lunds Universitet

A μ-mode integrator for solving evolution equations in Kronecker form

Author(s): Marco Caliari; Fabio Cassini; Lukas Einkemmer; Alexander Ostermann; Franco Zivcovich
Published in: Journal of Computational Physics, Issue 14, 2022, ISSN 0021-9991
Publisher: Academic Press
DOI: 10.1016/j.jcp.2022.110989

A General Framework of Low Regularity Integrators

Author(s): Frédéric Rousset and Katharina Schratz
Published in: SIAM Journal on Numerical Analysis, 2021, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1371506

Time integrators for dispersive equations in the long wave regime

Author(s): Calvo, María Cabrera; Rousset, Frédéric; Schratz, Katharina
Published in: Mathematics of Computation, Issue 9, 2021, ISSN 1088-6842
Publisher: AMS
DOI: 10.1090/mcom/3745

Convergence error estimates at low regularity for time discretizations of KdV

Author(s): Frédéric Rousset; Katharina Schratz
Published in: Pure and applied analysis, Issue 12, 2022, ISSN 2578-5885
Publisher: msp
DOI: 10.2140/paa.2022.4.127

"BAMPHI: Matrix-free and transpose-free action of linear combinations of <mml:math xmlns:mml=""http://www.w3.org/1998/Math/MathML"" display=""inline"" id=""d1e360"" altimg=""si2.svg""><mml:mi>φ</mml:mi></mml:math>-functions from exponential integrators"

Author(s): Marco Caliari; Fabio Cassini; Franco Zivcovich
Published in: Journal of Computational and Applied Mathematics, Issue 5, 2023, ISSN 0377-0427
Publisher: Elsevier BV
DOI: 10.1016/j.cam.2022.114973

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