Katharina Schratz

Publication Activity (10 Years)

Years Active: 2013-2024
Publications (10 Years): 46

Top Topics

Numerical Integration

Error Estimates

Top Venues

SIAM J. Numer. Anal.

J. Comput. Appl. Math.

Publications

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) (2024)
Frédéric Rousset, Katharina Schratz
Resonances as a computational tool. CoRR (2024)
Tianyu Jin, Georg Maierhofer, Katharina Schratz, Yang Xiang
A fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics. CoRR (2024)
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 (2024)
Valeria Banica, Georg Maierhofer, Katharina Schratz
Numerical Integration of Schrödinger Maps via the Hasimoto Transform. SIAM J. Numer. Anal. 62 (1) (2024)
Lun Ji, Alexander Ostermann, Frédéric Rousset, Katharina Schratz
Low regularity error estimates for the time integration of 2D NLS. CoRR (2023)
Lun Ji, Alexander Ostermann, Frédéric Rousset, Katharina Schratz
Low regularity full error estimates for the cubic nonlinear Schrödinger equation. CoRR (2023)
Yue Feng, Georg Maierhofer, Katharina Schratz
Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations. CoRR (2023)
Yvonne Alama Bronsard, Yvain Bruned, Georg Maierhofer, Katharina Schratz
Symmetric resonance based integrators and forest formulae. CoRR (2023)
Yue Feng, Georg Maierhofer, Katharina Schratz
Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations. Math. Comput. 93 (348) (2023)
Buyang Li, Katharina Schratz, Franco Zivcovich
A second-order low-regularity correction of Lie splitting for the semilinear Klein-Gordon equation. CoRR (2022)
Yue Feng, Katharina Schratz
Improved uniform error bounds on a Lawson-type exponential integrator for the long-time dynamics of sine-Gordon equation. CoRR (2022)
Georg Maierhofer, Katharina Schratz
Bridging the gap: symplecticity and low regularity on the example of the KdV equation. CoRR (2022)
Cao-Kha Doan, Thi-Thao-Phuong Hoang, Lili Ju, Katharina Schratz
Low regularity integrators for semilinear parabolic equations with maximum bound principles. CoRR (2022)
María Cabrera Calvo, Frédéric Rousset, Katharina Schratz
Time integrators for dispersive equations in the long wave regime. Math. Comput. 91 (337) (2022)
Yvonne Alama Bronsard, Yvain Bruned, Katharina Schratz
Approximations of dispersive PDEs in the presence of low-regularity randomness. CoRR (2022)
Buyang Li, Shu Ma, Katharina Schratz
A Semi-implicit Exponential Low-Regularity Integrator for the Navier-Stokes Equations. SIAM J. Numer. Anal. 60 (4) (2022)
Valeria Banica, Georg Maierhofer, Katharina Schratz
Numerical integration of Schrödinger maps via the Hasimoto transform. CoRR (2022)
Yvonne Alama Bronsard, Yvain Bruned, Katharina Schratz
Low regularity integrators via decorated trees. CoRR (2022)
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) (2022)
Alexander Ostermann, Frédéric Rousset, Katharina Schratz
Error estimates at low regularity of splitting schemes for NLS. Math. Comput. 91 (333) (2022)
Karolina Kropielnicka, Karolina Lademann, Katharina Schratz
Effective high order integrators for linear Klein-Gordon equations in low to highly oscillatory regimes. CoRR (2021)
Frédéric Rousset, Katharina Schratz
A General Framework of Low Regularity Integrators. SIAM J. Numer. Anal. 59 (3) (2021)
Frédéric Rousset, Katharina Schratz
Convergence error estimates at low regularity for time discretizations of KdV. CoRR (2021)
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 (2021)
Alexander Ostermann, Frédéric Rousset, Katharina Schratz
Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity. Found. Comput. Math. 21 (3) (2021)
María Cabrera Calvo, Katharina Schratz
Uniformly accurate splitting schemes for the Benjamin-Bona-Mahony equation with dispersive parameter. CoRR (2021)
María Cabrera Calvo, Frédéric Rousset, Katharina Schratz
Time integrators for dispersive equations in the long wave regime. CoRR (2021)
Buyang Li, Shu Ma, Katharina Schratz
A semi-implicit low-regularity integrator for Navier-Stokes equations. CoRR (2021)
Arieh Iserles, Karolina Kropielnicka, Katharina Schratz, Marcus Webb
Solving the linear semiclassical Schrödinger equation on the real line. CoRR (2021)
Katharina Schratz, Yan Wang, Xiaofei Zhao
Low-regularity integrators for nonlinear Dirac equations. Math. Comput. 90 (327) (2021)
María Cabrera Calvo, Katharina Schratz
Uniformly accurate low regularity integrators for the Klein-Gordon equation from the classical to non-relativistic limit regime. CoRR (2021)
Frédéric Rousset, Katharina Schratz
A general framework of low regularity integrators. CoRR (2020)
Alexander Ostermann, Frédéric Rousset, Katharina Schratz
Error estimates at low regularity of splitting schemes for NLS. CoRR (2020)
Yvain Bruned, Katharina Schratz
Resonance based schemes for dispersive equations via decorated trees. CoRR (2020)
Alexander Ostermann, Frédéric Rousset, Katharina Schratz
Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces. CoRR (2020)
Alexandre Poulain, Katharina Schratz
Convergence, error analysis and longtime behavior of the Scalar Auxiliary Variable method for the nonlinear Schrödinger equation. CoRR (2020)
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) (2019)
Katharina Schratz, Yan Wang, Xiaofei Zhao
Low-regularity integrators for nonlinear Dirac equations. CoRR (2019)
Marvin Knöller, Alexander Ostermann, Katharina Schratz
A Fourier Integrator for the Cubic Nonlinear Schrödinger Equation with Rough Initial Data. SIAM J. Numer. Anal. 57 (4) (2019)
Ludwig Gauckler, Jianfeng Lu, Jeremy Louis Marzuola, Frederic Rousset, Katharina Schratz
Trigonometric integrators for quasilinear wave equations. Math. Comput. 88 (316) (2019)
Alexander Ostermann, Katharina Schratz
Low Regularity Exponential-Type Integrators for Semilinear Schrödinger Equations. Found. Comput. Math. 18 (3) (2018)
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) (2018)
Martina Hofmanová, Katharina Schratz
An exponential-type integrator for the KdV equation. Numerische Mathematik 136 (4) (2017)
Patrick Krämer, Katharina Schratz
Efficient time integration of the Maxwell-Klein-Gordon equation in the non-relativistic limit regime. J. Comput. Appl. Math. 316 (2017)
Eskil Hansen, Alexander Ostermann, Katharina Schratz
The error structure of the Douglas-Rachford splitting method for stiff linear problems. J. Comput. Appl. Math. 303 (2016)
Erwan Faou, Katharina Schratz
Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime. Numerische Mathematik 126 (3) (2014)
Alexander Ostermann, Katharina Schratz
Stability of Exponential Operator Splitting Methods for Noncontractive Semigroups. SIAM J. Numer. Anal. 51 (1) (2013)