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## Ostermann, Alexander

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 Author ID: ostermann.alexander Published as: Ostermann, Alexander; Ostermann, A. Homepage: https://numerical-analysis.uibk.ac.at/staff/alexander-ostermann External Links: MGP · dblp
 Documents Indexed: 109 Publications since 1986, including 5 Books
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#### Co-Authors

 6 single-authored 13 Einkemmer, Lukas 11 Hochbruck, Marlis 10 Hansen, Eskil 8 Thalhammer, Mechthild 7 Caliari, Marco 7 Lubich, Christian 7 Schratz, Katharina 6 Rainer, Stefan 5 Luan, Vu Thai 5 Oberguggenberger, Michael B. 4 Piazzola, Chiara 3 Gu, Xian-Ming 3 Kandolf, Peter 3 Kaps, Peter 3 Zhao, Yongliang 2 Fellin, Wolfgang 2 González, Cesáreo 2 Hairer, Ernst 2 Hell, Tobias 2 Honig, Michael L. 2 Koskela, Antti 2 Mena, Hermann 2 Palencia, Cesar 2 Su, Chunmei 2 Wanner, Gerhard 1 Altmann, Robert 1 Bakaev, Nikolai Yu. 1 Brunner, Hermann 1 Faou, Erwan 1 Ganzález, Cesáreo 1 Hipp, David 1 Huang, Ting-Zhu 1 Husty, Manfred L. 1 Jian, Huanyan 1 Kauthen, Jean-Paul 1 Kirchner, Gerhard 1 Kirlinger, Gabriela 1 Knöller, Marvin 1 Koch, Herbert 1 Kofler, Andreas 1 Kramer, Felix 1 Leibold, Jan 1 Levajković, Tijana 1 Li, Meng 1 Moccaldi, Martina 1 Netzer, Norbert 1 Nicaise, Serge 1 Oh, Sung-Jin 1 Pauer, Franz 1 Pfurtscheller, Lena-Maria 1 Residori, Mirko 1 Rousset, Frédéric 1 Sandbichler, Michael 1 Schnaubelt, Roland 1 Schweitzer, Julia 1 Spielberger, G. 1 Tributsch, Alexander 1 Van Daele, Marnix 1 Walach, Hanna 1 Zhan, Rui 1 Zhao, Jingjun
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#### Serials

 12 Applied Numerical Mathematics 11 SIAM Journal on Numerical Analysis 9 BIT 9 Journal of Computational and Applied Mathematics 8 IMA Journal of Numerical Analysis 6 Mathematics of Computation 5 Computers & Mathematics with Applications 5 Numerische Mathematik 4 SIAM Journal on Scientific Computing 3 Journal of Computational Physics 2 International Journal for Numerical and Analytical Methods in Geomechanics 2 Applied Mathematics and Computation 2 Internationale Mathematische Nachrichten 2 Journal of Scientific Computing 2 Foundations of Computational Mathematics 2 Oberwolfach Reports 2 Undergraduate Topics in Computer Science 1 Inverse Problems 1 Journal of Mathematical Analysis and Applications 1 Mathematische Semesterberichte 1 ACM Transactions on Mathematical Software 1 Computing 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Integral Equations and Applications 1 Elemente der Mathematik 1 Linear Algebra and its Applications 1 ETNA. Electronic Transactions on Numerical Analysis 1 Discrete and Continuous Dynamical Systems 1 Mathematical and Computer Modelling of Dynamical Systems 1 Journal of Evolution Equations 1 Discrete and Continuous Dynamical Systems. Series B 1 Acta Numerica 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Undergraduate Texts in Mathematics
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#### Fields

 95 Numerical analysis (65-XX) 59 Partial differential equations (35-XX) 30 Ordinary differential equations (34-XX) 8 General and overarching topics; collections (00-XX) 7 Operator theory (47-XX) 4 Real functions (26-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Computer science (68-XX) 3 History and biography (01-XX) 3 Fluid mechanics (76-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Geometry (51-XX) 2 Probability theory and stochastic processes (60-XX) 2 Mechanics of deformable solids (74-XX) 2 Quantum theory (81-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

91 Publications have been cited 1,513 times in 828 Documents Cited by Year
Exponential integrators. Zbl 1242.65109
Hochbruck, Marlis; Ostermann, Alexander
2010
Explicit exponential Runge-Kutta methods for semilinear parabolic problems. Zbl 1093.65052
Hochbruck, Marlis; Ostermann, Alexander
2005
Exponential Runge-Kutta methods for parabolic problems. Zbl 1070.65099
Hochbruck, Marlis; Ostermann, Alexander
2005
Exponential Rosenbrock-type methods. Zbl 1193.65119
Hochbruck, Marlis; Ostermann, Alexander; Schweitzer, Julia
2009
Runge-Kutta methods for parabolic equations and convolution quadrature. Zbl 0795.65062
Lubich, Ch.; Ostermann, A.
1993
Multi-grid dynamic iteration for parabolic equations. Zbl 0623.65125
Lubich, Ch.; Ostermann, A.
1987
A class of explicit exponential general linear methods. Zbl 1103.65061
Ostermann, A.; Thalhammer, M.; Wright, W. M.
2006
Linearly implicit time discretization of nonlinear parabolic equations. Zbl 0834.65092
Lubich, Ch.; Ostermann, A.
1995
Runge-Kutta approximation of quasi-linear parabolic equations. Zbl 0832.65104
Lubich, Christian; Ostermann, Alexander
1995
High order splitting methods for analytic semigroups exist. Zbl 1176.65066
Hansen, Eskil; Ostermann, Alexander
2009
Implementation of exponential Rosenbrock-type integrators. Zbl 1160.65318
Caliari, Marco; Ostermann, Alexander
2009
Runge-Kutta methods for partial differential equations and fractional orders of convergence. Zbl 0769.65068
Ostermann, A.; Roche, M.
1992
Exponential splitting for unbounded operators. Zbl 1198.65185
Hansen, Eskil; Ostermann, Alexander
2009
Exponential multistep methods of Adams-type. Zbl 1237.65071
Hochbruck, Marlis; Ostermann, Alexander
2011
Explicit exponential Runge-Kutta methods of high order for parabolic problems. Zbl 1314.65103
Luan, Vu Thai; Ostermann, Alexander
2014
Rosenbrock methods for partial differential equations and fractional orders of convergence. Zbl 0780.65056
Ostermann, A.; Roche, M.
1993
Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: Nonsmooth-data error estimates and applications to long-time behaviour. Zbl 0872.65090
Lubich, Christian; Ostermann, Alexander
1996
A minimisation approach for computing the ground state of Gross-Pitaevskii systems. Zbl 1159.82311
Caliari, Marco; Ostermann, Alexander; Rainer, Stefan; Thalhammer, Mechthild
2009
Comparison of software for computing the action of the matrix exponential. Zbl 1290.65042
Caliari, Marco; Kandolf, Peter; Ostermann, Alexander; Rainer, Stefan
2014
Exponential Rosenbrock methods of order five – construction, analysis and numerical comparisons. Zbl 1291.65201
Luan, Vu Thai; Ostermann, Alexander
2014
Convergence of Runge-Kutta methods for nonlinear parabolic equations. Zbl 1004.65093
Ostermann, Alexander; Thalhammer, Mechthild
2002
The Leja method revisited: backward error analysis for the matrix exponential. Zbl 1339.65061
Caliari, Marco; Kandolf, Peter; Ostermann, Alexander; Rainer, Stefan
2016
Overcoming order reduction in diffusion-reaction splitting. I: Dirichlet boundary conditions. Zbl 1433.65189
Einkemmer, Lukas; Ostermann, Alexander
2015
Exponential B-series: the stiff case. Zbl 1285.65043
Luan, Vu Thai; Ostermann, Alexander
2013
Dimension splitting for evolution equations. Zbl 1149.65084
Hansen, Eskil; Ostermann, Alexander
2008
Numerical low-rank approximation of matrix differential equations. Zbl 1432.65090
Mena, Hermann; Ostermann, Alexander; Pfurtscheller, Lena-Maria; Piazzola, Chiara
2018
Interior estimates for time discretizations of parabolic equations. Zbl 0841.65080
Lubich, Christian; Ostermann, Alexander
1995
Backward Euler discretization of fully nonlinear parabolic problems. Zbl 0991.65087
González, Cesáreo; Ostermann, Alexander; Palencia, César; Thalhammer, Mechthild
2002
A second-order Magnus-type integrator for nonautonomous parabolic problems. Zbl 1089.65043
González, Cesáreo; Ostermann, A.; Thalhammer, Mechthild
2006
A second-order positivity preserving scheme for semilinear parabolic problems. Zbl 1267.65082
Hansen, Eskil; Kramer, Felix; Ostermann, Alexander
2012
Low regularity exponential-type integrators for semilinear Schrödinger equations. Zbl 1402.65098
Ostermann, Alexander; Schratz, Katharina
2018
Convergence analysis of Strang splitting for Vlasov-type equations. Zbl 1297.65106
Einkemmer, Lukas; Ostermann, Alexander
2014
Convergence analysis of a discontinuous Galerkin/Strang splitting approximation for the Vlasov-Poisson equations. Zbl 1302.82108
Einkemmer, Lukas; Ostermann, Alexander
2014
Non-smooth data error estimates for linearly implicit Runge-Kutta methods. Zbl 0954.65060
Ostermann, Alexander; Thalhammer, Mechthild
2000
The solution of a combustion problem with Rosenbrock methods. Zbl 0619.76088
Ostermann, A.; Kaps, P.; Bui, T. D.
1986
A splitting approach for the Kadomtsev-Petviashvili equation. Zbl 1354.65102
Einkemmer, Lukas; Ostermann, Alexander
2015
Overcoming order reduction in diffusion-reaction splitting. II: Oblique boundary conditions. Zbl 1355.65121
Einkemmer, Lukas; Ostermann, Alexander
2016
Geometry by its history. Zbl 1288.51001
Ostermann, Alexander; Wanner, Gerhard
2012
A class of half-explicit Runge-Kutta methods for differential-algebraic systems of index 3. Zbl 0788.65084
Ostermann, Alexander
1993
Analysis of exponential splitting methods for inhomogeneous parabolic equations. Zbl 1311.65118
Faou, Erwan; Ostermann, Alexander; Schratz, Katharina
2015
Stability of linear multistep methods and applications to nonlinear parabolic problems. Zbl 1041.65073
Ostermann, A.; Thalhammer, M.; Kirlinger, G.
2004
Rosenbrock methods using few LU-decompositions. Zbl 0667.65066
Kaps, Peter; Ostermann, Alexander
1989
A splitting approach for the magnetic Schrödinger equation. Zbl 1373.81195
Caliari, M.; Ostermann, A.; Piazzola, C.
2017
Hopf bifurcation of reaction-diffusion and Navier-Stokes equations under discretization. Zbl 0924.65051
Lubich, Christian; Ostermann, Alexander
1998
Runge-Kutta time discretizations of parabolic Volterra integro- differential equations. Zbl 0832.65141
Brunner, H.; Kauthen, J.-P.; Ostermann, A.
1995
A Fourier integrator for the cubic nonlinear Schrödinger equation with rough initial data. Zbl 1422.65222
Knöller, Marvin; Ostermann, Alexander; Schratz, Katharina
2019
An exponential integrator for non-autonomous parabolic problems. Zbl 1312.65210
Hipp, David; Hochbruck, Marlis; Ostermann, Alexander
2014
Modification of dimension-splitting methods – overcoming the order reduction due to corner singularities. Zbl 1321.65132
Hell, Tobias; Ostermann, Alexander; Sandbichler, Michael
2015
Dense output for extrapolation methods. Zbl 0693.65048
Hairer, Ernst; Ostermann, Alexander
1990
Error analysis of splitting methods for inhomogeneous evolution equations. Zbl 1267.65085
Ostermann, Alexander; Schratz, Katharina
2012
Convergence of a low-rank Lie-Trotter splitting for stiff matrix differential equations. Zbl 1420.65072
Ostermann, Alexander; Piazzola, Chiara; Walach, Hanna
2019
Dimension splitting for quasilinear parabolic equations. Zbl 1211.65117
Hansen, Eskil; Ostermann, Alexander
2010
Shadowing for nonautonomous parabolic problems with applications to long-time error bounds. Zbl 0954.35099
Ostermann, Alexander; Palencia, Cesar
2000
Long-term stability of variable stepsize approximations of semigroups. Zbl 1005.65076
Bakaev, Nikolai; Ostermann, Alexander
2002
Consistent tangent operators for constitutive rate equations. Zbl 1033.74043
Fellin, Wolfgang; Ostermann, Alexander
2002
Exponential Taylor methods: analysis and implementation. Zbl 1319.65120
Koskela, Antti; Ostermann, Alexander
2013
Meshfree exponential integrators. Zbl 1264.65164
Caliari, Marco; Ostermann, Alexander; Rainer, Stefan
2013
A residual based error estimate for Leja interpolation of matrix functions. Zbl 1293.65075
Kandolf, Peter; Ostermann, Alexander; Rainer, Stefan
2014
A convergence analysis of the exponential Euler iteration for nonlinear ill-posed problems. Zbl 1184.65063
Hochbruck, Marlis; Hönig, Michael; Ostermann, Alexander
2009
Positivity of exponential multistep methods. Zbl 1119.65357
Ostermann, Alexander; Thalhammer, Mechthild
2006
Continuous extensions of Rosenbrock-type methods. Zbl 0697.65055
Ostermann, Alexander
1990
A half-explicit extrapolation method for differential-algebraic systems of index 3. Zbl 0704.65051
Ostermann, Alexander
1990
Parallel exponential Rosenbrock methods. Zbl 1443.65093
Luan, Vu Thai; Ostermann, Alexander
2016
On the error propagation of semi-Lagrange and Fourier methods for advection problems. Zbl 1364.65179
Einkemmer, Lukas; Ostermann, Alexander
2015
An almost symmetric Strang splitting scheme for nonlinear evolution equations. Zbl 1368.65074
Einkemmer, Lukas; Ostermann, Alexander
2014
Stability analysis of explicit exponential integrators for delay differential equations. Zbl 1348.65113
Zhao, Jingjun; Zhan, Rui; Ostermann, Alexander
2016
High-order splitting schemes for semilinear evolution equations. Zbl 1355.65071
Hansen, Eskil; Ostermann, Alexander
2016
Stability of exponential operator splitting methods for noncontractive semigroups. Zbl 1274.65217
Ostermann, Alexander; Schratz, Katharina
2013
Positivity of exponential Runge-Kutta methods. Zbl 1125.65068
Ostermann, Alexander; van Daele, Marnix
2007
Stability of W-methods with applications to operator splitting and to geometric theory. Zbl 1007.65063
Ostermann, Alexander
2002
Dimension splitting for time dependent operators. Zbl 1189.65104
Hansen, Eskil; Ostermann, Alexander
2009
An almost symmetric Strang splitting scheme for the construction of high order composition methods. Zbl 1321.65109
Einkemmer, Lukas; Ostermann, Alexander
2014
Splitting methods for constrained diffusion-reaction systems. Zbl 1391.35228
Altmann, R.; Ostermann, A.
2017
Detecting structural changes with ARMA processes. Zbl 1348.93243
Ostermann, A.; Spielberger, G.; Tributsch, A.
2016
Dense output for the GBS extrapolation method. Zbl 0810.65074
Hairer, E.; Ostermann, A.
1992
Compatibility conditions for Dirichlet and Neumann problems of Poisson’s equation on a rectangle. Zbl 1298.35050
Hell, Tobias; Ostermann, Alexander
2014
Regularization of nonlinear ill-posed problems by exponential integrators. Zbl 1167.65369
Hochbruck, Marlis; Hönig, Michael; Ostermann, Alexander
2009
Optimal convergence results for Runge-Kutta discretizations of linear nonautonomous parabolic problems. Zbl 0921.65068
Ganzález, Cesáreo; Ostermann, Alexander
1999
A comparison of boundary correction methods for Strang splitting. Zbl 1397.65155
Einkemmer, Lukas; Ostermann, Alexander
2018
Two exponential-type integrators for the “good” Boussinesq equation. Zbl 1428.35425
Ostermann, Alexander; Su, Chunmei
2019
Efficient boundary corrected Strang splitting. Zbl 1427.65087
Einkemmer, Lukas; Moccaldi, Martina; Ostermann, Alexander
2018
A low-rank projector-splitting integrator for the Vlasov-Maxwell equations with divergence correction. Zbl 1453.65357
Einkemmer, Lukas; Ostermann, Alexander; Piazzola, Chiara
2020
On the convergence of Lawson methods for semilinear stiff problems. Zbl 1453.65269
Hochbruck, Marlis; Leibold, Jan; Ostermann, Alexander
2020
Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity. Zbl 07371332
Ostermann, Alexander; Rousset, Frédéric; Schratz, Katharina
2021
The error structure of the Douglas-Rachford splitting method for stiff linear problems. Zbl 1382.65151
Hansen, Eskil; Ostermann, Alexander; Schratz, Katharina
2016
$$L(\alpha{})$$-stable variable order Rosenbrock methods. Zbl 0738.65064
Kaps, Peter; Ostermann, Alexander
1991
Finite element Runge-Kutta discretizations of porous medium-type equations. Zbl 1169.76033
Hansen, Eskil; Ostermann, Alexander
2008
Reprint of “Explicit exponential Runge-Kutta methods of high order for parabolic problems”. Zbl 1330.65111
Luan, Vu Thai; Ostermann, Alexander
2014
A dynamic proof of Thébault’s theorem. Zbl 1192.51011
Ostermann, Alexander; Wanner, Gerhard
2010
Unconditional convergence of DIRK schemes applied to dissipative evolution equations. Zbl 1193.65138
Hansen, Eskil; Ostermann, Alexander
2010
A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev-Petviashvili equation. Zbl 1427.65285
Einkemmer, Lukas; Ostermann, Alexander
2018
Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity. Zbl 07371332
Ostermann, Alexander; Rousset, Frédéric; Schratz, Katharina
2021
A low-rank projector-splitting integrator for the Vlasov-Maxwell equations with divergence correction. Zbl 1453.65357
Einkemmer, Lukas; Ostermann, Alexander; Piazzola, Chiara
2020
On the convergence of Lawson methods for semilinear stiff problems. Zbl 1453.65269
Hochbruck, Marlis; Leibold, Jan; Ostermann, Alexander
2020
A Fourier integrator for the cubic nonlinear Schrödinger equation with rough initial data. Zbl 1422.65222
Knöller, Marvin; Ostermann, Alexander; Schratz, Katharina
2019
Convergence of a low-rank Lie-Trotter splitting for stiff matrix differential equations. Zbl 1420.65072
Ostermann, Alexander; Piazzola, Chiara; Walach, Hanna
2019
Two exponential-type integrators for the “good” Boussinesq equation. Zbl 1428.35425
Ostermann, Alexander; Su, Chunmei
2019
Numerical low-rank approximation of matrix differential equations. Zbl 1432.65090
Mena, Hermann; Ostermann, Alexander; Pfurtscheller, Lena-Maria; Piazzola, Chiara
2018
Low regularity exponential-type integrators for semilinear Schrödinger equations. Zbl 1402.65098
Ostermann, Alexander; Schratz, Katharina
2018
A comparison of boundary correction methods for Strang splitting. Zbl 1397.65155
Einkemmer, Lukas; Ostermann, Alexander
2018
Efficient boundary corrected Strang splitting. Zbl 1427.65087
Einkemmer, Lukas; Moccaldi, Martina; Ostermann, Alexander
2018
A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev-Petviashvili equation. Zbl 1427.65285
Einkemmer, Lukas; Ostermann, Alexander
2018
A splitting approach for the magnetic Schrödinger equation. Zbl 1373.81195
Caliari, M.; Ostermann, A.; Piazzola, C.
2017
Splitting methods for constrained diffusion-reaction systems. Zbl 1391.35228
Altmann, R.; Ostermann, A.
2017
The Leja method revisited: backward error analysis for the matrix exponential. Zbl 1339.65061
Caliari, Marco; Kandolf, Peter; Ostermann, Alexander; Rainer, Stefan
2016
Overcoming order reduction in diffusion-reaction splitting. II: Oblique boundary conditions. Zbl 1355.65121
Einkemmer, Lukas; Ostermann, Alexander
2016
Parallel exponential Rosenbrock methods. Zbl 1443.65093
Luan, Vu Thai; Ostermann, Alexander
2016
Stability analysis of explicit exponential integrators for delay differential equations. Zbl 1348.65113
Zhao, Jingjun; Zhan, Rui; Ostermann, Alexander
2016
High-order splitting schemes for semilinear evolution equations. Zbl 1355.65071
Hansen, Eskil; Ostermann, Alexander
2016
Detecting structural changes with ARMA processes. Zbl 1348.93243
Ostermann, A.; Spielberger, G.; Tributsch, A.
2016
The error structure of the Douglas-Rachford splitting method for stiff linear problems. Zbl 1382.65151
Hansen, Eskil; Ostermann, Alexander; Schratz, Katharina
2016
Overcoming order reduction in diffusion-reaction splitting. I: Dirichlet boundary conditions. Zbl 1433.65189
Einkemmer, Lukas; Ostermann, Alexander
2015
A splitting approach for the Kadomtsev-Petviashvili equation. Zbl 1354.65102
Einkemmer, Lukas; Ostermann, Alexander
2015
Analysis of exponential splitting methods for inhomogeneous parabolic equations. Zbl 1311.65118
Faou, Erwan; Ostermann, Alexander; Schratz, Katharina
2015
Modification of dimension-splitting methods – overcoming the order reduction due to corner singularities. Zbl 1321.65132
Hell, Tobias; Ostermann, Alexander; Sandbichler, Michael
2015
On the error propagation of semi-Lagrange and Fourier methods for advection problems. Zbl 1364.65179
Einkemmer, Lukas; Ostermann, Alexander
2015
Explicit exponential Runge-Kutta methods of high order for parabolic problems. Zbl 1314.65103
Luan, Vu Thai; Ostermann, Alexander
2014
Comparison of software for computing the action of the matrix exponential. Zbl 1290.65042
Caliari, Marco; Kandolf, Peter; Ostermann, Alexander; Rainer, Stefan
2014
Exponential Rosenbrock methods of order five – construction, analysis and numerical comparisons. Zbl 1291.65201
Luan, Vu Thai; Ostermann, Alexander
2014
Convergence analysis of Strang splitting for Vlasov-type equations. Zbl 1297.65106
Einkemmer, Lukas; Ostermann, Alexander
2014
Convergence analysis of a discontinuous Galerkin/Strang splitting approximation for the Vlasov-Poisson equations. Zbl 1302.82108
Einkemmer, Lukas; Ostermann, Alexander
2014
An exponential integrator for non-autonomous parabolic problems. Zbl 1312.65210
Hipp, David; Hochbruck, Marlis; Ostermann, Alexander
2014
A residual based error estimate for Leja interpolation of matrix functions. Zbl 1293.65075
Kandolf, Peter; Ostermann, Alexander; Rainer, Stefan
2014
An almost symmetric Strang splitting scheme for nonlinear evolution equations. Zbl 1368.65074
Einkemmer, Lukas; Ostermann, Alexander
2014
An almost symmetric Strang splitting scheme for the construction of high order composition methods. Zbl 1321.65109
Einkemmer, Lukas; Ostermann, Alexander
2014
Compatibility conditions for Dirichlet and Neumann problems of Poisson’s equation on a rectangle. Zbl 1298.35050
Hell, Tobias; Ostermann, Alexander
2014
Reprint of “Explicit exponential Runge-Kutta methods of high order for parabolic problems”. Zbl 1330.65111
Luan, Vu Thai; Ostermann, Alexander
2014
Exponential B-series: the stiff case. Zbl 1285.65043
Luan, Vu Thai; Ostermann, Alexander
2013
Exponential Taylor methods: analysis and implementation. Zbl 1319.65120
Koskela, Antti; Ostermann, Alexander
2013
Meshfree exponential integrators. Zbl 1264.65164
Caliari, Marco; Ostermann, Alexander; Rainer, Stefan
2013
Stability of exponential operator splitting methods for noncontractive semigroups. Zbl 1274.65217
Ostermann, Alexander; Schratz, Katharina
2013
A second-order positivity preserving scheme for semilinear parabolic problems. Zbl 1267.65082
Hansen, Eskil; Kramer, Felix; Ostermann, Alexander
2012
Geometry by its history. Zbl 1288.51001
Ostermann, Alexander; Wanner, Gerhard
2012
Error analysis of splitting methods for inhomogeneous evolution equations. Zbl 1267.65085
Ostermann, Alexander; Schratz, Katharina
2012
Exponential multistep methods of Adams-type. Zbl 1237.65071
Hochbruck, Marlis; Ostermann, Alexander
2011
Exponential integrators. Zbl 1242.65109
Hochbruck, Marlis; Ostermann, Alexander
2010
Dimension splitting for quasilinear parabolic equations. Zbl 1211.65117
Hansen, Eskil; Ostermann, Alexander
2010
A dynamic proof of Thébault’s theorem. Zbl 1192.51011
Ostermann, Alexander; Wanner, Gerhard
2010
Unconditional convergence of DIRK schemes applied to dissipative evolution equations. Zbl 1193.65138
Hansen, Eskil; Ostermann, Alexander
2010
Exponential Rosenbrock-type methods. Zbl 1193.65119
Hochbruck, Marlis; Ostermann, Alexander; Schweitzer, Julia
2009
High order splitting methods for analytic semigroups exist. Zbl 1176.65066
Hansen, Eskil; Ostermann, Alexander
2009
Implementation of exponential Rosenbrock-type integrators. Zbl 1160.65318
Caliari, Marco; Ostermann, Alexander
2009
Exponential splitting for unbounded operators. Zbl 1198.65185
Hansen, Eskil; Ostermann, Alexander
2009
A minimisation approach for computing the ground state of Gross-Pitaevskii systems. Zbl 1159.82311
Caliari, Marco; Ostermann, Alexander; Rainer, Stefan; Thalhammer, Mechthild
2009
A convergence analysis of the exponential Euler iteration for nonlinear ill-posed problems. Zbl 1184.65063
Hochbruck, Marlis; Hönig, Michael; Ostermann, Alexander
2009
Dimension splitting for time dependent operators. Zbl 1189.65104
Hansen, Eskil; Ostermann, Alexander
2009
Regularization of nonlinear ill-posed problems by exponential integrators. Zbl 1167.65369
Hochbruck, Marlis; Hönig, Michael; Ostermann, Alexander
2009
Dimension splitting for evolution equations. Zbl 1149.65084
Hansen, Eskil; Ostermann, Alexander
2008
Finite element Runge-Kutta discretizations of porous medium-type equations. Zbl 1169.76033
Hansen, Eskil; Ostermann, Alexander
2008
Positivity of exponential Runge-Kutta methods. Zbl 1125.65068
Ostermann, Alexander; van Daele, Marnix
2007
A class of explicit exponential general linear methods. Zbl 1103.65061
Ostermann, A.; Thalhammer, M.; Wright, W. M.
2006
A second-order Magnus-type integrator for nonautonomous parabolic problems. Zbl 1089.65043
González, Cesáreo; Ostermann, A.; Thalhammer, Mechthild
2006
Positivity of exponential multistep methods. Zbl 1119.65357
Ostermann, Alexander; Thalhammer, Mechthild
2006
Explicit exponential Runge-Kutta methods for semilinear parabolic problems. Zbl 1093.65052
Hochbruck, Marlis; Ostermann, Alexander
2005
Exponential Runge-Kutta methods for parabolic problems. Zbl 1070.65099
Hochbruck, Marlis; Ostermann, Alexander
2005
Stability of linear multistep methods and applications to nonlinear parabolic problems. Zbl 1041.65073
Ostermann, A.; Thalhammer, M.; Kirlinger, G.
2004
Convergence of Runge-Kutta methods for nonlinear parabolic equations. Zbl 1004.65093
Ostermann, Alexander; Thalhammer, Mechthild
2002
Backward Euler discretization of fully nonlinear parabolic problems. Zbl 0991.65087
González, Cesáreo; Ostermann, Alexander; Palencia, César; Thalhammer, Mechthild
2002
Long-term stability of variable stepsize approximations of semigroups. Zbl 1005.65076
Bakaev, Nikolai; Ostermann, Alexander
2002
Consistent tangent operators for constitutive rate equations. Zbl 1033.74043
Fellin, Wolfgang; Ostermann, Alexander
2002
Stability of W-methods with applications to operator splitting and to geometric theory. Zbl 1007.65063
Ostermann, Alexander
2002
Non-smooth data error estimates for linearly implicit Runge-Kutta methods. Zbl 0954.65060
Ostermann, Alexander; Thalhammer, Mechthild
2000
Shadowing for nonautonomous parabolic problems with applications to long-time error bounds. Zbl 0954.35099
Ostermann, Alexander; Palencia, Cesar
2000
Optimal convergence results for Runge-Kutta discretizations of linear nonautonomous parabolic problems. Zbl 0921.65068
Ganzález, Cesáreo; Ostermann, Alexander
1999
Hopf bifurcation of reaction-diffusion and Navier-Stokes equations under discretization. Zbl 0924.65051
Lubich, Christian; Ostermann, Alexander
1998
Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: Nonsmooth-data error estimates and applications to long-time behaviour. Zbl 0872.65090
Lubich, Christian; Ostermann, Alexander
1996
Linearly implicit time discretization of nonlinear parabolic equations. Zbl 0834.65092
Lubich, Ch.; Ostermann, A.
1995
Runge-Kutta approximation of quasi-linear parabolic equations. Zbl 0832.65104
Lubich, Christian; Ostermann, Alexander
1995
Interior estimates for time discretizations of parabolic equations. Zbl 0841.65080
Lubich, Christian; Ostermann, Alexander
1995
Runge-Kutta time discretizations of parabolic Volterra integro- differential equations. Zbl 0832.65141
Brunner, H.; Kauthen, J.-P.; Ostermann, A.
1995
Runge-Kutta methods for parabolic equations and convolution quadrature. Zbl 0795.65062
Lubich, Ch.; Ostermann, A.
1993
Rosenbrock methods for partial differential equations and fractional orders of convergence. Zbl 0780.65056
Ostermann, A.; Roche, M.
1993
A class of half-explicit Runge-Kutta methods for differential-algebraic systems of index 3. Zbl 0788.65084
Ostermann, Alexander
1993
Runge-Kutta methods for partial differential equations and fractional orders of convergence. Zbl 0769.65068
Ostermann, A.; Roche, M.
1992
Dense output for the GBS extrapolation method. Zbl 0810.65074
Hairer, E.; Ostermann, A.
1992
$$L(\alpha{})$$-stable variable order Rosenbrock methods. Zbl 0738.65064
Kaps, Peter; Ostermann, Alexander
1991
Dense output for extrapolation methods. Zbl 0693.65048
Hairer, Ernst; Ostermann, Alexander
1990
Continuous extensions of Rosenbrock-type methods. Zbl 0697.65055
Ostermann, Alexander
1990
A half-explicit extrapolation method for differential-algebraic systems of index 3. Zbl 0704.65051
Ostermann, Alexander
1990
Rosenbrock methods using few LU-decompositions. Zbl 0667.65066
Kaps, Peter; Ostermann, Alexander
1989
Multi-grid dynamic iteration for parabolic equations. Zbl 0623.65125
Lubich, Ch.; Ostermann, A.
1987
The solution of a combustion problem with Rosenbrock methods. Zbl 0619.76088
Ostermann, A.; Kaps, P.; Bui, T. D.
1986
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#### Cited by 1,041 Authors

 54 Ostermann, Alexander 21 Wu, Xinyuan 19 Lubich, Christian 17 Einkemmer, Lukas 17 Wang, Bin 14 Ju, Lili 13 Caliari, Marco 13 Hochbruck, Marlis 13 Schratz, Katharina 13 Thalhammer, Mechthild 12 Cano, Begoña 12 Hansen, Eskil 12 Khaliq, Abdul Q. M. 10 Alonso-Mallo, Isaías 10 Blanes, Sergio 10 Zhao, Jingjun 9 Akrivis, Georgios D. 9 López-Fernández, María 9 Luan, Vu Thai 9 Sandu, Adrian 9 Tambue, Antoine 8 Bao, Weizhu 8 Palencia, Cesar 8 Xu, Yang 7 Cai, Yongyong 7 Csomós, Petra 7 Garrappa, Roberto 7 González, Cesáreo 7 Klein, Christian 7 Liu, Changying 7 Mena, Hermann 7 Rang, Joachim 7 Tokman, Mayya 6 Chartier, Philippe 6 Faou, Erwan 6 Gander, Martin Jakob 6 Jorge, Juan Carlos 6 Kandolf, Peter 6 Li, Buyang 6 Li, Xiao 6 Moret, Igor 6 Mukam, Jean Daniel 6 Sauter, Stefan A. 6 Sayas, Francisco-Javier 6 Vilmart, Gilles 6 Weiner, Rüdiger 6 Zhan, Rui 6 Zhao, Xiaofei 5 Auzinger, Winfried 5 Burrage, Kevin 5 Casas, Fernando 5 Crouseilles, Nicolas 5 Emmrich, Etienne 5 Geiser, Jürgen 5 Hairer, Ernst 5 Koch, Othmar 5 Kovács, Mihály 5 Moreta, María Jesús 5 Reguera, Nuria 5 Rodrigo, Carmen 5 Seydaoğlu, Muaz 5 Simoncini, Valeria 5 Stillfjord, Tony 5 Su, Chunmei 5 Wade, Bruce A. 5 Wanner, Gerhard 5 Wensch, Jörg 4 Altmann, Robert 4 Banjai, Lehel 4 Bátkai, András 4 Bhatt, Harish P. 4 Calvo, M. P. 4 Du, Qiang 4 Furati, Khaled M. 4 Gaspar, Francisco José 4 Gauckler, Ludwig J. 4 González-Pinto, Severiano 4 Hernandez-Abreu, Domingo 4 Iserles, Arieh 4 Jahnke, Tobias 4 Kovács, Balázs 4 Lang, Jens 4 Li, Dongping 4 Lord, Gabriel James 4 Mei, Lijie 4 Novati, Paolo 4 Owolabi, Kolade Matthew 4 Popolizio, Marina 4 Qiao, Zhonghua 4 Rainer, Stefan 4 Rainwater, Greg 4 Rousset, Frédéric 4 Schnaubelt, Roland 4 Söderlind, Gustaf 4 Turner, Ian William 4 Wang, Cheng 3 Arévalo, Carmen 3 Bader, Philipp 3 Baumstark, Simon 3 Bujanda, Blanca ...and 941 more Authors
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#### Cited in 139 Serials

 83 Applied Numerical Mathematics 75 Journal of Computational Physics 75 Journal of Computational and Applied Mathematics 53 BIT 48 Numerische Mathematik 44 SIAM Journal on Scientific Computing 32 Computers & Mathematics with Applications 31 Mathematics of Computation 31 SIAM Journal on Numerical Analysis 28 Journal of Scientific Computing 25 Applied Mathematics and Computation 18 Numerical Algorithms 11 Computer Methods in Applied Mechanics and Engineering 10 Foundations of Computational Mathematics 9 International Journal of Computer Mathematics 8 Applied Mathematics Letters 8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 7 Journal of Mathematical Analysis and Applications 7 Numerical Methods for Partial Differential Equations 6 Linear Algebra and its Applications 6 Discrete and Continuous Dynamical Systems. Series B 5 Mathematics and Computers in Simulation 5 Physica D 5 Numerical Linear Algebra with Applications 5 Discrete and Continuous Dynamical Systems 4 Calcolo 4 Computational Mechanics 4 SIAM Journal on Matrix Analysis and Applications 4 Elemente der Mathematik 4 Computational and Applied Mathematics 4 Advances in Computational Mathematics 3 Computers and Fluids 3 Computer Physics Communications 3 Computing 3 International Journal for Numerical Methods in Engineering 3 Numerical Functional Analysis and Optimization 3 Journal of Integral Equations and Applications 3 Japan Journal of Industrial and Applied Mathematics 3 Applied Mathematical Modelling 3 Abstract and Applied Analysis 3 Communications in Nonlinear Science and Numerical Simulation 3 Journal of Applied Mathematics and Computing 3 Multiscale Modeling & Simulation 3 East Asian Journal on Applied Mathematics 2 Wave Motion 2 Journal of Functional Analysis 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Semigroup Forum 2 SIAM Review 2 Journal of Nonlinear Science 2 ETNA. Electronic Transactions on Numerical Analysis 2 Computing and Visualization in Science 2 Computational Geosciences 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 Journal of Evolution Equations 2 Computational Methods in Applied Mathematics 2 Journal of Applied Mathematics 2 Journal of Numerical Mathematics 2 International Journal of Differential Equations 2 Research in the Mathematical Sciences 2 SN Partial Differential Equations and Applications 1 Analysis Mathematica 1 Communications in Mathematical Physics 1 International Journal of Control 1 International Journal for Numerical and Analytical Methods in Geomechanics 1 International Journal for Numerical Methods in Fluids 1 Inverse Problems 1 Journal of Fluid Mechanics 1 Journal of Mathematical Physics 1 The Mathematical Gazette 1 Mathematical Methods in the Applied Sciences 1 Mathematische Semesterberichte 1 Nonlinearity 1 The Mathematical Intelligencer 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Probability 1 Automatica 1 Czechoslovak Mathematical Journal 1 Integral Equations and Operator Theory 1 Transactions of the American Mathematical Society 1 Acta Applicandae Mathematicae 1 ACM Transactions on Graphics 1 COMPEL 1 Science in China. Series A 1 Applications of Mathematics 1 Computational Mathematics and Mathematical Physics 1 Stochastic Processes and their Applications 1 Indagationes Mathematicae. New Series 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Journal of Mathematical Sciences (New York) 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Engineering Analysis with Boundary Elements 1 Bernoulli 1 Journal of Mathematical Chemistry 1 Mathematical Problems in Engineering 1 Optimization Methods & Software 1 Journal of Inequalities and Applications 1 Journal of Applied Mechanics and Technical Physics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences ...and 39 more Serials
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#### Cited in 45 Fields

 747 Numerical analysis (65-XX) 363 Partial differential equations (35-XX) 163 Ordinary differential equations (34-XX) 62 Fluid mechanics (76-XX) 42 Dynamical systems and ergodic theory (37-XX) 38 Operator theory (47-XX) 30 Linear and multilinear algebra; matrix theory (15-XX) 26 Quantum theory (81-XX) 24 Probability theory and stochastic processes (60-XX) 23 Statistical mechanics, structure of matter (82-XX) 22 Integral equations (45-XX) 21 Mechanics of deformable solids (74-XX) 18 Optics, electromagnetic theory (78-XX) 17 Systems theory; control (93-XX) 16 Biology and other natural sciences (92-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Mechanics of particles and systems (70-XX) 11 Geophysics (86-XX) 10 Real functions (26-XX) 10 Classical thermodynamics, heat transfer (80-XX) 8 Geometry (51-XX) 6 Special functions (33-XX) 6 Integral transforms, operational calculus (44-XX) 6 Computer science (68-XX) 4 Approximations and expansions (41-XX) 4 Functional analysis (46-XX) 3 History and biography (01-XX) 3 Difference and functional equations (39-XX) 3 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 Algebraic geometry (14-XX) 2 Topological groups, Lie groups (22-XX) 2 Differential geometry (53-XX) 2 Statistics (62-XX) 2 Operations research, mathematical programming (90-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX)