Stability of Exponential Operator Splitting Methods for Noncontractive Semigroups. - Alexander Ostermann; Katharina Schratz (SIAM J. Numer. Anal., 2013)

Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime. - Erwan Faou; Katharina Schratz (Numerische Mathematik, 2014)

The error structure of the Douglas-Rachford splitting method for stiff linear problems. - Eskil Hansen; Alexander Ostermann; Katharina Schratz (J. Comput. Appl. Math., 2016)

Efficient time integration of the Maxwell-Klein-Gordon equation in the non-relativistic limit regime. - Patrick Krämer; Katharina Schratz (J. Comput. Appl. Math., 2017)

An exponential-type integrator for the KdV equation. - Martina Hofmanová; Katharina Schratz (Numerische Mathematik, 2017)

Low Regularity Exponential-Type Integrators for Semilinear Schrödinger Equations. - Alexander Ostermann; Katharina Schratz (Found. Comput. Math., 2018)

Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting. - Simon Baumstark; Erwan Faou; Katharina Schratz (Math. Comput., 2018)

Trigonometric integrators for quasilinear wave equations. - Ludwig Gauckler; Jianfeng Lu 001; Jeremy Louis Marzuola; Frederic Rousset; Katharina Schratz (Math. Comput., 2019)

Uniformly Accurate Oscillatory Integrators for the Klein-Gordon-Zakharov System from Low- to High-Plasma Frequency Regimes. - Simon Baumstark; Katharina Schratz (SIAM J. Numer. Anal., 2019)

A Fourier Integrator for the Cubic Nonlinear Schrödinger Equation with Rough Initial Data. - Marvin Knöller; Alexander Ostermann; Katharina Schratz (SIAM J. Numer. Anal., 2019)

Resonance based schemes for dispersive equations via decorated trees. - Yvain Bruned; Katharina Schratz (CoRR, 2020)

Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces. - Alexander Ostermann; Frédéric Rousset; Katharina Schratz (CoRR, 2020)

Convergence, error analysis and longtime behavior of the Scalar Auxiliary Variable method for the nonlinear Schrödinger equation. - Alexandre Poulain; Katharina Schratz (CoRR, 2020)

Solving the linear semiclassical Schrödinger equation on the real line. - Arieh Iserles; Karolina Kropielnicka; Katharina Schratz; Marcus Webb (CoRR, 2021)

Convergence error estimates at low regularity for time discretizations of KdV. - Frédéric Rousset; Katharina Schratz (CoRR, 2021)

Uniformly accurate low regularity integrators for the Klein-Gordon equation from the classical to non-relativistic limit regime. - María Cabrera Calvo; Katharina Schratz (CoRR, 2021)

Uniformly accurate splitting schemes for the Benjamin-Bona-Mahony equation with dispersive parameter. - María Cabrera Calvo; Katharina Schratz (CoRR, 2021)

A semi-implicit low-regularity integrator for Navier-Stokes equations. - Buyang Li; Shu Ma; Katharina Schratz (CoRR, 2021)

Effective high order integrators for linear Klein-Gordon equations in low to highly oscillatory regimes. - Karolina Kropielnicka; Karolina Lademann; Katharina Schratz (CoRR, 2021)

Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity. - Alexander Ostermann; Frédéric Rousset; Katharina Schratz (Found. Comput. Math., 2021)

Splitting methods for nonlinear Dirac equations with Thirring type interaction in the nonrelativistic limit regime. - Patrick Krämer; Katharina Schratz; Xiaofei Zhao (J. Comput. Appl. Math., 2021)

Low-regularity integrators for nonlinear Dirac equations. - Katharina Schratz; Yan Wang; Xiaofei Zhao (Math. Comput., 2021)

A General Framework of Low Regularity Integrators. - Frédéric Rousset; Katharina Schratz (SIAM J. Numer. Anal., 2021)

Low regularity integrators via decorated trees. - Yvonne Alama Bronsard; Yvain Bruned; Katharina Schratz (CoRR, 2022)

A second-order low-regularity correction of Lie splitting for the semilinear Klein-Gordon equation. - Buyang Li; Katharina Schratz; Franco Zivcovich (CoRR, 2022)

Bridging the gap: symplecticity and low regularity on the example of the KdV equation. - Georg Maierhofer; Katharina Schratz (CoRR, 2022)

Low regularity integrators for semilinear parabolic equations with maximum bound principles. - Cao-Kha Doan; Thi-Thao-Phuong Hoang; Lili Ju; Katharina Schratz (CoRR, 2022)

Time integrators for dispersive equations in the long wave regime. - María Cabrera Calvo; Frédéric Rousset; Katharina Schratz (Math. Comput., 2022)

Error estimates at low regularity of splitting schemes for NLS. - Alexander Ostermann; Frédéric Rousset; Katharina Schratz (Math. Comput., 2022)

Uniformly Accurate Low Regularity Integrators for the Klein-Gordon Equation from the Classical to NonRelativistic Limit Regime. - María Cabrera Calvo; Katharina Schratz (SIAM J. Numer. Anal., 2022)

A Semi-implicit Exponential Low-Regularity Integrator for the Navier-Stokes Equations. - Buyang Li; Shu Ma; Katharina Schratz (SIAM J. Numer. Anal., 2022)

Low regularity error estimates for the time integration of 2D NLS. - Lun Ji; Alexander Ostermann; Frédéric Rousset; Katharina Schratz (CoRR, 2023)

Symmetric resonance based integrators and forest formulae. - Yvonne Alama Bronsard; Yvain Bruned; Georg Maierhofer; Katharina Schratz (CoRR, 2023)

Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations. - Yue Feng; Georg Maierhofer; Katharina Schratz (Math. Comput., 2023)

Resonances as a computational tool. - Frédéric Rousset; Katharina Schratz (CoRR, 2024)

G-Adaptive mesh refinement - leveraging graph neural networks and differentiable finite element solvers. - James Rowbottom; Georg Maierhofer; Teo Deveney; Katharina Schratz; Pietro Liò; Carola-Bibiane Schönlieb; Chris J. Budd (CoRR, 2024)

Long-term error analysis of low-regularity integrators for stochastic Schrödinger equations. - Stefano Di Giovacchino; Katharina Schratz (CoRR, 2024)

Computing rough solutions of the stochastic nonlinear wave equation. - Jiachuan Cao; Buyang Li; Katharina Schratz (CoRR, 2024)

Low Regularity Full Error Estimates for the Cubic Nonlinear Schrödinger Equation. - Lun Ji; Alexander Ostermann; Frédéric Rousset; Katharina Schratz (SIAM J. Numer. Anal., 2024)

Numerical Integration of Schrödinger Maps via the Hasimoto Transform. - Valeria Banica; Georg Maierhofer; Katharina Schratz (SIAM J. Numer. Anal., 2024)

Improved uniform error bounds on a Lawson-type exponential integrator for the long-time dynamics of sine-Gordon equation. - Yue Feng; Katharina Schratz (Numerische Mathematik, 2024)

Approximations of Dispersive PDEs in the Presence of Low-Regularity Randomness. - Yvonne Alama Bronsard; Yvain Bruned; Katharina Schratz (Found. Comput. Math., 2024)

A fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics. - Tianyu Jin; Georg Maierhofer; Katharina Schratz; Yang Xiang (J. Comput. Phys., 2025)

Resonances and computations. - Yvain Bruned; Frédéric Rousset; Katharina Schratz (CoRR, 2025)

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation. - Erwan Faou; Georg Maierhofer; Katharina Schratz (CoRR, 2025)

Effective highly accurate time integrators for linear Klein-Gordon equations across the scales. - Karolina Kropielnicka; Karolina Lademann; Katharina Schratz (J. Num. Math., 2025)