Hermitesche Differenzenverfahren zur Approximation der Lösung von Differentialgleichungen der Formuxy=f(x, y, u, ux, uy). - Alexander Ostermann (Computing, 1977)

The solution of a combustion problem with Rosenbrock methods. - Alexander Ostermann; Peter Kaps; Tien Dai Bui (ACM Trans. Math. Softw., 1986)

Continuous extensions of Rosenbrock-type methods. - Alexander Ostermann (Computing, 1990)

Hopf bifurcation of reaction-diffusion and Navier-Stokes equations under discretization. - Christian Lubich; Alexander Ostermann (Numerische Mathematik, 1998)

Shadowing for Nonautonomous Parabolic Problems with Applications to Long-Time Error Bounds. - Alexander Ostermann; Cesar Palencia (SIAM J. Numer. Anal., 2000)

Long-term stability of variable stepsize approximations of semigroups. - Nikolai Bakaev; Alexander Ostermann (Math. Comput., 2002)

Backward Euler discretization of fully nonlinear parabolic problems. - Cesáreo González; Alexander Ostermann; Cesar Palencia; Mechthild Thalhammer (Math. Comput., 2002)

Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems. - Marlis Hochbruck; Alexander Ostermann (SIAM J. Numer. Anal., 2005)

Dimension splitting for evolution equations. - Eskil Hansen; Alexander Ostermann (Numerische Mathematik, 2008)

Finite Element Runge-Kutta Discretizations of Porous Medium-Type Equations. - Eskil Hansen; Alexander Ostermann (SIAM J. Numer. Anal., 2008)

Exponential Rosenbrock-Type Methods. - Marlis Hochbruck; Alexander Ostermann; Julia Schweitzer (SIAM J. Numer. Anal., 2008)

A minimisation approach for computing the ground state of Gross-Pitaevskii systems. - Marco Caliari; Alexander Ostermann; Stefan Rainer; Mechthild Thalhammer (J. Comput. Phys., 2009)

Exponential splitting for unbounded operators. - Eskil Hansen; Alexander Ostermann (Math. Comput., 2009)

Exponential integrators. - Marlis Hochbruck; Alexander Ostermann (Acta Numer., 2010)

Analysis for Computer Scientists - Foundations, Methods, and Algorithms. - Michael Oberguggenberger; Alexander Ostermann (Springer, 2011)

Stiff Order Conditions for Exponential Runge-Kutta Methods of Order Five. - Vu Thai Luan; Alexander Ostermann (HPSC, 2012)

Exponential integrators on graphic processing units. - Lukas Einkemmer; Alexander Ostermann (HPCS, 2013)

Exponential Taylor methods: Analysis and implementation. - Antti Koskela; Alexander Ostermann (Comput. Math. Appl., 2013)

Exponential B-Series: The Stiff Case. - Vu Thai Luan; Alexander Ostermann (SIAM J. Numer. Anal., 2013)

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

Meshfree Exponential Integrators. - Marco Caliari; Alexander Ostermann; Stefan Rainer (SIAM J. Sci. Comput., 2013)

An almost symmetric Strang splitting scheme for nonlinear evolution equations. - Lukas Einkemmer; Alexander Ostermann (Comput. Math. Appl., 2014)

An almost symmetric Strang splitting scheme for the construction of high order composition methods. - Lukas Einkemmer; Alexander Ostermann (J. Comput. Appl. Math., 2014)

Explicit exponential Runge-Kutta methods of high order for parabolic problems. - Vu Thai Luan; Alexander Ostermann (J. Comput. Appl. Math., 2014)

Exponential Rosenbrock methods of order five - construction, analysis and numerical comparisons. - Vu Thai Luan; Alexander Ostermann (J. Comput. Appl. Math., 2014)

Reprint of "Explicit exponential Runge-Kutta methods of high order for parabolic problems". - Vu Thai Luan; Alexander Ostermann (J. Comput. Appl. Math., 2014)

A Moment-Matching Arnoldi Iteration for Linear Combinations of φ Functions. - Antti Koskela; Alexander Ostermann (SIAM J. Matrix Anal. Appl., 2014)

Convergence Analysis of Strang Splitting for Vlasov-Type Equations. - Lukas Einkemmer; Alexander Ostermann (SIAM J. Numer. Anal., 2014)

Convergence Analysis of a Discontinuous Galerkin/Strang Splitting Approximation for the Vlasov-Poisson Equations. - Lukas Einkemmer; Alexander Ostermann (SIAM J. Numer. Anal., 2014)

On the error propagation of semi-Lagrange and Fourier methods for advection problems. - Lukas Einkemmer; Alexander Ostermann (Comput. Math. Appl., 2015)

Fast algorithms for morphological operations using run-length encoded binary images. - Gregor Ehrensperger; Alexander Ostermann; Felix Schwitzer (CoRR, 2015)

A splitting approach for the Kadomtsev-Petviashvili equation. - Lukas Einkemmer; Alexander Ostermann (J. Comput. Phys., 2015)

Overcoming Order Reduction in Diffusion-Reaction Splitting. Part 1: Dirichlet Boundary Conditions. - Lukas Einkemmer; Alexander Ostermann (SIAM J. Sci. Comput., 2015)

Parallel exponential Rosenbrock methods. - Vu Thai Luan; Alexander Ostermann (Comput. Math. Appl., 2016)

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

Evaluation of the partitioned global address space (PGAS) model for an inviscid Euler solver. - Martina Prugger; Lukas Einkemmer; Alexander Ostermann (Parallel Comput., 2016)

The Leja Method Revisited: Backward Error Analysis for the Matrix Exponential. - Marco Caliari; Peter Kandolf; Alexander Ostermann; Stefan Rainer (SIAM J. Sci. Comput., 2016)

Overcoming Order Reduction in Diffusion-Reaction Splitting. Part 2: Oblique Boundary Conditions. - Lukas Einkemmer; Alexander Ostermann (SIAM J. Sci. Comput., 2016)

Splitting methods for constrained diffusion-reaction systems. - Robert Altmann; Alexander Ostermann (Comput. Math. Appl., 2017)

A splitting approach for the magnetic Schrödinger equation. - Marco Caliari; Alexander Ostermann; Chiara Piazzola (J. Comput. Appl. Math., 2017)

Efficient boundary corrected Strang splitting. - Lukas Einkemmer; Martina Moccaldi; Alexander Ostermann (Appl. Math. Comput., 2018)

A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev-Petviashvili equation. - Lukas Einkemmer; Alexander Ostermann (Appl. Math. Comput., 2018)

Magnus integrators on multicore CPUs and GPUs. - N. Auer; Lukas Einkemmer; Peter Kandolf; Alexander Ostermann (Comput. Phys. Commun., 2018)

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

Numerical low-rank approximation of matrix differential equations. - Hermann Mena; Alexander Ostermann; Lena-Maria Pfurtscheller; Chiara Piazzola (J. Comput. Appl. Math., 2018)

Analysis for Computer Scientists - Foundations, Methods, and Algorithms, Second Edition - Michael Oberguggenberger; Alexander Ostermann (Springer, 2018)

Two exponential-type integrators for the "good" Boussinesq equation. - Alexander Ostermann; Chunmei Su (Numerische Mathematik, 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)

Convergence of a Low-Rank Lie-Trotter Splitting for Stiff Matrix Differential Equations. - Alexander Ostermann; Chiara Piazzola; Hanna Walach (SIAM J. Numer. Anal., 2019)

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

A parallel preconditioning technique for an all-at-once system from subdiffusion equations with variable time steps. - Yong-Liang Zhao; Xian-Ming Gu; Alexander Ostermann (CoRR, 2020)

An efficient second-order energy stable BDF scheme for the space fractional Cahn-Hilliard equation. - Yong-Liang Zhao; Meng Li 025; Alexander Ostermann; Xian-Ming Gu (CoRR, 2020)

A low-rank projector-splitting integrator for the Vlasov-Maxwell equations with divergence correction. - Lukas Einkemmer; Alexander Ostermann; Chiara Piazzola (J. Comput. Phys., 2020)

On the convergence of Lawson methods for semilinear stiff problems. - Marlis Hochbruck; Jan Leibold; Alexander Ostermann (Numerische Mathematik, 2020)

Fast numerical schemes for nonlinear space-fractional multidelay reaction-diffusion equations by implicit integration factor methods. - Huan-Yan Jian; Ting-Zhu Huang; Alexander Ostermann; Xian-Ming Gu; Yong-Liang Zhao (Appl. Math. Comput., 2021)

A μ-mode integrator for solving evolution equations in Kronecker form. - Marco Caliari; Fabio Cassini; Lukas Einkemmer; Alexander Ostermann; Franco Zivcovich (CoRR, 2021)

A second order low-regularity integrator for the nonlinear Schrödinger equation. - Alexander Ostermann; Fangyan Yao; Yifei Wu (CoRR, 2021)

An exponential integrator/WENO discretization for sonic-boom simulation on modern computer hardware. - Lukas Einkemmer; Alexander Ostermann; Mirko Residori (Comput. Phys. Commun., 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)

A pseudo-spectral splitting method for linear dispersive problems with transparent boundary conditions. - Lukas Einkemmer; Alexander Ostermann; Mirko Residori (J. Comput. Appl. Math., 2021)

An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs. - Marco Caliari; Lukas Einkemmer; Alexander Moriggl; Alexander Ostermann (J. Comput. Phys., 2021)

A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations. - Yong-Liang Zhao; Alexander Ostermann; Xian-Ming Gu (J. Comput. Phys., 2021)

Fast IIF-WENO Method on Non-uniform Meshes for Nonlinear Space-Fractional Convection-Diffusion-Reaction Equations. - Huan-Yan Jian; Ting-Zhu Huang; Alexander Ostermann; Xian-Ming Gu; Yong-Liang Zhao (J. Sci. Comput., 2021)

A Preconditioning Technique for an All-at-once System from Volterra Subdiffusion Equations with Graded Time Steps. - Yong-Liang Zhao; Xian-Ming Gu; Alexander Ostermann (J. Sci. Comput., 2021)

A μ-mode integrator for solving evolution equations in Kronecker form. - Marco Caliari; Fabio Cassini; Lukas Einkemmer; Alexander Ostermann; Franco Zivcovich (J. Comput. Phys., 2022)

A Fully Discrete Low-Regularity Integrator for the Nonlinear Schrödinger Equation. - Alexander Ostermann; Fangyan Yao (J. Sci. Comput., 2022)

Exponential Integrators for Second-Order in Time Partial Differential Equations. - Duy Phan; Alexander Ostermann (J. Sci. Comput., 2022)

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

A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions. - Lukas Einkemmer; Alexander Ostermann; Mirko Residori (Numerische Mathematik, 2022)

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

Accelerating exponential integrators to efficiently solve advection-diffusion-reaction equations. - Marco Caliari; Fabio Cassini; Lukas Einkemmer; Alexander Ostermann (CoRR, 2023)

Low regularity error estimates for high dimensional nonlinear Schrödinger equations. - Lun Ji; Alexander Ostermann (CoRR, 2023)

Explicit Exponential Runge-Kutta Methods for Semilinear Integro-Differential Equations. - Alexander Ostermann; Fardin Saedpanah; Nasrin Vaisi (SIAM J. Numer. Anal., 2023)

A robust and conservative dynamical low-rank algorithm. - Lukas Einkemmer; Alexander Ostermann; Carmela Scalone (J. Comput. Phys., 2023)

The exponential trapezoidal method for semilinear integro-differential equations. - Alexander Ostermann; Nasrin Vaisi (CoRR, 2024)

Should exponential integrators be used for advection-dominated problems? - Lukas Einkemmer; Trung Hau Hoang; Alexander Ostermann (CoRR, 2024)

Highly efficient NURBS-based isogeometric analysis for coupled nonlinear diffusion-reaction equations with and without advection. - Ilham Asmouh; Alexander Ostermann (J. Comput. Sci., 2024)

Filtered Lie-Trotter splitting for the "good" Boussinesq equation: Low regularity error estimates. - Lun Ji; Hang Li; Alexander Ostermann; Chunmei Su (Math. Comput., 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)

Accelerating Exponential Integrators to Efficiently Solve Semilinear Advection-Diffusion-Reaction Equations. - Marco Caliari; Fabio Cassini; Lukas Einkemmer; Alexander Ostermann (SIAM J. Sci. Comput., 2024)

An initial-corrected splitting approach for convection-diffusion-reaction problems. - Thi Tam Dang; Lukas Einkemmer; Alexander Ostermann (CoRR, 2025)

Exponential Runge-Kutta methods of collocation type for parabolic equations with time-dependent delay. - Qiumei Huang; Alexander Ostermann; Gangfan Zhong (CoRR, 2025)

On the convergence of split exponential integrators for semilinear parabolic problems. - Marco Caliari; Fabio Cassini; Lukas Einkemmer; Alexander Ostermann (CoRR, 2025)

An initial-boundary corrected splitting method for diffusion-reaction problems. - Thi Tam Dang; Lukas Einkemmer; Alexander Ostermann (CoRR, 2025)

Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators. - Qiumei Huang; Alexander Ostermann; Gangfan Zhong (CoRR, 2025)