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Katharina Schratz
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2020 – today
- 2024
- [j22]Yue Feng, Katharina Schratz:
Improved uniform error bounds on a Lawson-type exponential integrator for the long-time dynamics of sine-Gordon equation. Numerische Mathematik 156(4): 1455-1477 (2024) - [j21]Valeria Banica, Georg Maierhofer
, Katharina Schratz:
Numerical Integration of Schrödinger Maps via the Hasimoto Transform. SIAM J. Numer. Anal. 62(1): 322-352 (2024) - [j20]Lun Ji
Low Regularity Full Error Estimates for the Cubic Nonlinear Schrödinger Equation. SIAM J. Numer. Anal. 62(5): 2071-2086 (2024) - [i28]Frédéric Rousset, Katharina Schratz:
Resonances as a computational tool. CoRR abs/2405.10572 (2024) - [i27]Tianyu Jin, Georg Maierhofer, Katharina Schratz, Yang Xiang:
A fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics. CoRR abs/2407.03945 (2024) - [i26]James Rowbottom, Georg Maierhofer, Teo Deveney, Katharina Schratz, Pietro Liò, Carola-Bibiane Schönlieb, Chris J. Budd:
G-Adaptive mesh refinement - leveraging graph neural networks and differentiable finite element solvers. CoRR abs/2407.04516 (2024) - [i25]Stefano Di Giovacchino, Katharina Schratz:
Long-term error analysis of low-regularity integrators for stochastic Schrödinger equations. CoRR abs/2410.22201 (2024) - 2023
- [j19]Yue Feng, Georg Maierhofer, Katharina Schratz:
Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations. Math. Comput. 93(348): 1569-1598 (2023) - [i24]Lun Ji, Alexander Ostermann, Frédéric Rousset, Katharina Schratz:
Low regularity error estimates for the time integration of 2D NLS. CoRR abs/2301.10639 (2023) - [i23]Yue Feng, Georg Maierhofer, Katharina Schratz:
Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations. CoRR abs/2302.00383 (2023) - [i22]Yvonne Alama Bronsard, Yvain Bruned, Georg Maierhofer, Katharina Schratz:
Symmetric resonance based integrators and forest formulae. CoRR abs/2305.16737 (2023) - [i21]Lun Ji, Alexander Ostermann, Frédéric Rousset, Katharina Schratz:
Low regularity full error estimates for the cubic nonlinear Schrödinger equation. CoRR abs/2311.14366 (2023) - 2022
- [j18]Alexander Ostermann
Error estimates at low regularity of splitting schemes for NLS. Math. Comput. 91(333): 169-182 (2022) - [j17]María Cabrera Calvo, Frédéric Rousset, Katharina Schratz:
Time integrators for dispersive equations in the long wave regime. Math. Comput. 91(337): 2197-2214 (2022) - [j16]María Cabrera Calvo, Katharina Schratz:
Uniformly Accurate Low Regularity Integrators for the Klein-Gordon Equation from the Classical to NonRelativistic Limit Regime. SIAM J. Numer. Anal. 60(2): 888-912 (2022) - [j15]Buyang Li
A Semi-implicit Exponential Low-Regularity Integrator for the Navier-Stokes Equations. SIAM J. Numer. Anal. 60(4): 2273-2292 (2022) - [i20]Yvonne Alama Bronsard, Yvain Bruned, Katharina Schratz:
Low regularity integrators via decorated trees. CoRR abs/2202.01171 (2022) - [i19]Buyang Li, Katharina Schratz, Franco Zivcovich:
A second-order low-regularity correction of Lie splitting for the semilinear Klein-Gordon equation. CoRR abs/2203.15539 (2022) - [i18]Yvonne Alama Bronsard, Yvain Bruned, Katharina Schratz:
Approximations of dispersive PDEs in the presence of low-regularity randomness. CoRR abs/2205.02156 (2022) - [i17]Georg Maierhofer
Bridging the gap: symplecticity and low regularity on the example of the KdV equation. CoRR abs/2205.05024 (2022) - [i16]Valeria Banica, Georg Maierhofer
Numerical integration of Schrödinger maps via the Hasimoto transform. CoRR abs/2211.01282 (2022) - [i15]Cao-Kha Doan, Thi-Thao-Phuong Hoang, Lili Ju, Katharina Schratz:
Low regularity integrators for semilinear parabolic equations with maximum bound principles. CoRR abs/2211.03982 (2022) - [i14]Yue Feng, Katharina Schratz:
Improved uniform error bounds on a Lawson-type exponential integrator for the long-time dynamics of sine-Gordon equation. CoRR abs/2211.09402 (2022) - 2021
- [j14]Alexander Ostermann
Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity. Found. Comput. Math. 21(3): 725-765 (2021) - [j13]Patrick Krämer, Katharina Schratz, Xiaofei Zhao:
Splitting methods for nonlinear Dirac equations with Thirring type interaction in the nonrelativistic limit regime. J. Comput. Appl. Math. 387: 112494 (2021) - [j12]Katharina Schratz, Yan Wang, Xiaofei Zhao:
Low-regularity integrators for nonlinear Dirac equations. Math. Comput. 90(327): 189-214 (2021) - [j11]Frédéric Rousset, Katharina Schratz:
A General Framework of Low Regularity Integrators. SIAM J. Numer. Anal. 59(3): 1735-1768 (2021) - [i13]Arieh Iserles, Karolina Kropielnicka, Katharina Schratz, Marcus Webb:
Solving the linear semiclassical Schrödinger equation on the real line. CoRR abs/2102.00413 (2021) - [i12]Frédéric Rousset, Katharina Schratz:
Convergence error estimates at low regularity for time discretizations of KdV. CoRR abs/2102.11125 (2021) - [i11]María Cabrera Calvo, Katharina Schratz:
Uniformly accurate low regularity integrators for the Klein-Gordon equation from the classical to non-relativistic limit regime. CoRR abs/2104.11672 (2021) - [i10]María Cabrera Calvo, Frédéric Rousset, Katharina Schratz:
Time integrators for dispersive equations in the long wave regime. CoRR abs/2105.03731 (2021) - [i9]María Cabrera Calvo, Katharina Schratz:
Uniformly accurate splitting schemes for the Benjamin-Bona-Mahony equation with dispersive parameter. CoRR abs/2105.03732 (2021) - [i8]Buyang Li, Shu Ma, Katharina Schratz:
A semi-implicit low-regularity integrator for Navier-Stokes equations. CoRR abs/2107.13427 (2021) - [i7]Karolina Kropielnicka, Karolina Lademann, Katharina Schratz:
Effective high order integrators for linear Klein-Gordon equations in low to highly oscillatory regimes. CoRR abs/2112.08908 (2021) - 2020
- [i6]Yvain Bruned, Katharina Schratz:
Resonance based schemes for dispersive equations via decorated trees. CoRR abs/2005.01649 (2020) - [i5]Alexander Ostermann, Frédéric Rousset, Katharina Schratz:
Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces. CoRR abs/2006.12785 (2020) - [i4]Frédéric Rousset, Katharina Schratz:
A general framework of low regularity integrators. CoRR abs/2010.01640 (2020) - [i3]Alexandre Poulain, Katharina Schratz:
Convergence, error analysis and longtime behavior of the Scalar Auxiliary Variable method for the nonlinear Schrödinger equation. CoRR abs/2012.13943 (2020) - [i2]Alexander Ostermann, Frédéric Rousset, Katharina Schratz:
Error estimates at low regularity of splitting schemes for NLS. CoRR abs/2012.14146 (2020)
2010 – 2019
- 2019
- [j10]Ludwig Gauckler, Jianfeng Lu
Trigonometric integrators for quasilinear wave equations. Math. Comput. 88(316): 717-749 (2019) - [j9]Simon Baumstark, Katharina Schratz:
Uniformly Accurate Oscillatory Integrators for the Klein-Gordon-Zakharov System from Low- to High-Plasma Frequency Regimes. SIAM J. Numer. Anal. 57(1): 429-457 (2019) - [j8]Marvin Knöller, Alexander Ostermann
A Fourier Integrator for the Cubic Nonlinear Schrödinger Equation with Rough Initial Data. SIAM J. Numer. Anal. 57(4): 1967-1986 (2019) - [i1]Katharina Schratz, Yan Wang, Xiaofei Zhao:
Low-regularity integrators for nonlinear Dirac equations. CoRR abs/1906.09413 (2019) - 2018
- [j7]Alexander Ostermann, Katharina Schratz:
Low Regularity Exponential-Type Integrators for Semilinear Schrödinger Equations. Found. Comput. Math. 18(3): 731-755 (2018) - [j6]Simon Baumstark, Erwan Faou, Katharina Schratz:
Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting. Math. Comput. 87(311): 1227-1254 (2018) - 2017
- [j5]Patrick Krämer, Katharina Schratz:
Efficient time integration of the Maxwell-Klein-Gordon equation in the non-relativistic limit regime. J. Comput. Appl. Math. 316: 247-259 (2017) - [j4]Martina Hofmanová, Katharina Schratz:
An exponential-type integrator for the KdV equation. Numerische Mathematik 136(4): 1117-1137 (2017) - 2016
- [j3]Eskil Hansen
The error structure of the Douglas-Rachford splitting method for stiff linear problems. J. Comput. Appl. Math. 303: 140-145 (2016) - 2014
- [j2]Erwan Faou, Katharina Schratz:
Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime. Numerische Mathematik 126(3): 441-469 (2014) - 2013
- [j1]Alexander Ostermann
Stability of Exponential Operator Splitting Methods for Noncontractive Semigroups. SIAM J. Numer. Anal. 51(1): 191-203 (2013)
Coauthor Index
aka: Frédéric Rousset
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