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[ 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | 2004 | 2003 | 2002 | 2001 | 2000 | 1999 | 1998 | 1997 | 1996 | 1995 ]

2011

• Gerhard Dziuk, Christian Lubich, Dhia Mansour, Runge-Kutta time discretization of parabolic differential equations on evolving surfaces, IMA J. Numer. Anal. (2011), doi:10.1093/imanum/drr017.
• Lehel Banjai, Christian Lubich, Jens Markus Melenk, Runge-Kutta convolution quadrature for operators arising in wave propagation, Numer. Math. 119 (2011), 1-20.
• Lehel Banjai, Christian Lubich, An error analysis of Runge-Kutta convolution quadrature, BIT 51 (2011), 483-496.
• Nicola Guglielmi, Christian Lubich, Differential equations for roaming pseudospectra: paths to extremal points and boundary tracking, SIAM J. Numer. Anal. 49 (2011), 1194-1209. Erratum/Addendum.
• Othmar Koch, Christian Lubich, Variational-splitting time integration of the multi-configuration time-dependent Hartree-Fock equations in electron dynamics, IMA J. Numer. Anal. 31 (2011), 379-395.
• Ludwig Gauckler, Convergence of a split-step Hermite method for the Gross-Pitaevskii equation, IMA J. Numer. Anal. 31 (2011), 396-415.
• Jonas Haehnle, Andreas Prohl, Mumford-Shah-Euler Flow With Sphere Constraint And Applications to Colour Image Inpainting, SIAM J. Imaging Sci. 4 (2011), 1200-1233.
• Jonas Haehnle, Numerical Approximations of the Mumford-Shah Functional for Unit Vector Fields, IFBJ Volume 13, Issue 3 (2011), 297-326.

2010

• Christian Lubich, Benny Walther, Bernd Bruegmann, Symplectic integration of post-Newtonian equations of motion with spin, Phys. Rev. D 81 (2010), 104025.
• Dajana Conte, Christian Lubich, An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics, M2AN 44 (2010), 759-780.
• Othmar Koch, Christian Lubich, Dynamical tensor approximation, SIAM J. Matrix Anal. 31 (2010), 2360-2375.
• Erich Carelli, Jonas Haehnle, and Andreas Prohl, Convergence analysis for incompressible generalized Newtonian fluid flows with nonstandard anisotropic growth conditions, SIAM J. Numer. Anal. 48 (2010), 164-190.
• Jonas Haehnle, Andreas Prohl, Approximation of nonlinear wave equations with nonstandard anisotropic growth conditions, Math. Comp. 79 (2010), 189-208.
• Ludwig Gauckler, Christian Lubich, Splitting integrators for nonlinear Schrödinger equations over long times, Found. Comput. Math. 10 (2010), 275-302.
• Ludwig Gauckler, Christian Lubich, Nonlinear Schrödinger equations and their spectral semi-discretizations over long times, Found. Comput. Math. 10 (2010), 141-169.

2009

• Erwan Faou, Vasile Gradinaru, Christian Lubich, Computing semiclassical quantum dynamics with Hagedorn wavepackets, SIAM J. Sci. Comp. 31 (2009), 3027-3041.
• Sören Bartels, Christian Lubich, and Andreas Prohl, Convergent discretization of heat and wave map flows to spheres using approximate discrete Lagrange multipliers, Math. Comp. 78 (2009), 1269-1292.
• Ernst Hairer, Christian Lubich, Oscillations over long times in numerical Hamiltonian systems, in Highly oscillatory problems (B. Engquist, A. Fokas, E. Hairer, A. Iserles, eds.), London Mathematical Society Lecture Note Series 366, Cambridge Univ. Press, 2009.

2008

• Erwan Faou, Vasile Gradinaru, Gauss-Hermite wavepacket dynamics: convergence of the spectral and pseudo-spectral approximation, IMA Journal of Numerical Analysis 2008; doi: 10.1093/imanum/drn041.
• Ronny Richter, Christian Lubich, Free and constrained symplectic integrators for numerical general relativity, Class. Quantum Grav. 25 (2008), 225018.
• Achim Nonnenmacher, Christian Lubich, Dynamical low-rank approximation: applications and numerical experiments, Math. Comput. Simulation 79 (2008), 1346-1357.
• Christian Lubich, On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations, Math. Comp. 77 (2008), 2141-2153.
• David Cohen, Ernst Hairer, Christian Lubich, Conservation of energy, momentum and actions in numerical discretizations of nonlinear wave equations, Numer. Math. 110 (2008), 113-143.
• Ernst Hairer, Christian Lubich, Spectral semi-discretisations of weakly nonlinear wave equations over long times, Found. Comput. Math. 8 (2008), 319-334.
• David Cohen, Ernst Hairer, Christian Lubich, Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions, Arch. Ration. Mech. Anal. 187 (2008), 341-368.
• Maria Lopez-Fernandez, Christian Lubich, Achim Schädle, Adaptive, fast, and oblivious convolution in evolution equations with memory, SIAM J. Sci. Comp. 30 (2008), 1015-1037.

2007

• Vasile Gradinaru, Strang Splitting for the Time Dependent Schrödinger Equation on Sparse Grids, SIAM J. Num. Analysis 46 (2007), 103-123.
• Vasile Gradinaru, Fourier Transform on Sparse Grids: Code Design and Application to the Time Dependent Schrödinger Equation, Computing 80 (2007), 1-22.
• Othmar Koch, Christian Lubich, Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics, M2AN 41 (2007), 315-332.
• Othmar Koch, Christian Lubich, Dynamical low rank approximation, SIAM J. Matrix Anal. Appl. 29 (2007), 434-454.

2006

• David Cohen, Tobias Jahnke, Katina Lorenz, Christian Lubich, Numerical integrators for highly oscillatory Hamiltonian systems: a review, in Analysis, Modeling and Simulation of Multiscale Problems (A. Mielke, ed.), Springer, Berlin, 2006, 553-576.
• Erwan Faou and Christian Lubich, A Poisson integrator for Gaussian wavepacket dynamics, Comput. Vis. Sci. 9 (2006), 45-55.
• David Cohen, Conservation properties of numerical integrators for highly oscillatory Hamiltonian systems, IMA J. Numer. Anal. 26 (2006), 34-59.
• Achim Schädle, Maria Lopez-Fernandez, Christian Lubich, Fast and oblivious convolution quadrature, SIAM J. Sci. Comp. 28 (2006), 421-438.
• Eduardo Cuesta, Christian Lubich, Cesar Palencia, Convolution quadrature time discretization of fractional diffusion-wave equations, Math.Comp. 75 (2006), 673-696.

2005

• Maria Lopez-Fernandez, Christian Lubich, Cesar Palencia, Achim Schädle, Fast Runge-Kutta approximation of inhomogeneous parabolic equations, Numer. Math. 102 (2005), 277-291.
• David Cohen, Ernst Hairer, Christian Lubich, Numerical energy conservation for multi-frequency oscillatory differential equations, BIT 45 (2005), 287-305.
• Nicola Guglielmi, Christian Lubich, Numerical periodic orbits of neutral delay differential equations, Discrete Contin. Dyn. Syst. 13 (2005), 1057-1067.
• Katina Lorenz, Tobias Jahnke, Christian Lubich, Adiabatic integrators for highly oscillatory second order linear differential equations with time-varying eigendecomposition, BIT 45 (2005), 91-115.
• Christian Lubich, On variational approximations in quantum molecular dynamics, Math. Comp.74 (2005), 765-779.

2004

• Christian Lubich, Convolution quadrature revisited, BIT 44 (2004), 503-514.
• Ernst Hairer and Christian Lubich, Symmetric multistep methods over long times, Numer. Math. 97 (2004), 699-723.
• Christian Lubich, A variational splitting integrator for quantum molecular dynamics, Appl. Numer. Math. 48 (2004), 355-368.

2003

• David Cohen, Ernst Hairer and Christian Lubich, Modulated Fourier expansions of highly oscillatory differential equations, Foundations of Comput. Math. 3 (2003), 327-345.
• Ernst Hairer, Christian Lubich, Gerhard Wanner, Geometric numerical integration illustrated by the Störmer-Verlet method, Acta Numerica 2003, 399-450.
• Marlis Hochbruck and Christian Lubich, On Magnus integrators for time-dependent Schrödinger equations, SIAM J. Numer. Anal. 41 (2003), 945-963.
• Tobias Jahnke and Christian Lubich, Numerical integrators for quantum dynamics close to the adiabatic limit, Numer. Math. 94 (2003), 289-314.

2002

• Harry Yserentant, The convergence of the finite mass method for flows in given force and velocity fields, in: Meshfree Methods for Partial Differential Equations (M. Griebel and M.A. Schweitzer, eds.), Lecture Notes in Computational Science and Engineering 26 (2002).
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• Klaus Neymeyr, A geometric theory for preconditioned inverse iteration applied to a subspace, Math. Comp. 71 (2002), 197-216.
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• Christian Lubich, Integrators for quantum dynamics: a numerical analyst's brief review, in Quantum Simulations of Many-Body Systems: From Theory to Algorithms (J. Grotendorst, D. Marx, A. Muramatsu, eds.), NIC Series Vol. 10, Jülich 2002, 459-466.
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• Christian Lubich and Achim Schädle, Fast convolution for non-reflecting boundary conditions, SIAM J. Sci. Comput. 24 (2002), 161-182.
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• Achim Schädle, Non-reflecting boundary conditions for the two-dimensional Schrödinger equation, Wave Motion 35 (2002), 181-188.
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2001

• Christian Lubich, On dynamics and bifurcations of nonlinear evolution equations under numerical discretization, in B. Fiedler (ed.), Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, Springer, Berlin, 2001, 469-500.
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• Harry Yserentant, The propagation of sound in particle models of compressible fluids, Numer. Math. (2001) 88: 581-601
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• Klaus Neymeyr, A geometric theory for preconditioned inverse iteration, I:Extrema of the Rayleigh quotient, Linear Algebra Appl. 332 (2001), 61-85
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• Klaus Neymeyr, A geometric theory for preconditioned inverse iteration, II:Convergence estimates, Linear Algebra Appl. 332 (2001), 87-104
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2000

• Christoph Gauger, Peter Leinen, Harry Yserentant, The Finite Mass Method, November 1999. SIAM J. Numer. Anal. 37 (2000), 1768-1799
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• Tobias Jahnke, Christian Lubich, Error bounds for exponential operator splittings, BIT 40 (2000), 735-744.
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• Ernst Hairer, Christian Lubich, Energy conservation by Störmer-type numerical integrators, in Numerical Analysis 1999 (D.F. Griffiths, G.A. Watson, eds.), Chapman & Hall/CRC, London (2000), 169-190.
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• Ernst Hairer, Christian Lubich, Long-time energy conservation of numerical methods for oscillatory differential equations, SIAM J. Numer. Anal. 38 (2000), 414-441.
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• Ernst Hairer, Christian Lubich, Asymptotic expansions and backward analysis for numerical integrators, in Dynamics of Algorithms (R. de la Llave, L.R. Petzold, J. Lorenz, eds.), Springer IMA Vol. 118, 2000, 91-106.
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1999

• Harry Yserentant, Coarse grid spaces for domains with a complicated boundary, Numerical Algorithms 21 (1999), 387-392.
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• Marlis Hochbruck, Christian Lubich, Exponential integrators for quantum-classical molecular dynamics, BIT 39 (1999), 620-645.
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• Marlis Hochbruck, Christian Lubich, A Gautschi-type method for oscillatory second-order differential equations, Numer. Math. 83 (1999), 403-426.
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• Jos L.M. van Dorsselaer, Christian Lubich, Inertial manifolds of parabolic differential equations under higher-order discretizations, IMA J. Numer. Anal. 19 (1999), 455-471.
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• Harry Yserentant, Particles of variable size, Numer. Math., 82 (1999), pp. 143-159.
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• Harry Yserentant, Entropy generation and shock resolution in the particle model of compressible fluids, Numer. Math., 82 (1999), pp. 161-177.
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• Ernst Hairer, Christian Lubich, Invariant tori of dissipatively perturbed Hamiltonian systems under symplectic discretization, Appl. Numer. Math. 29 (1999), 57-71.
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• Marlis Hochbruck, Christian Lubich, A bunch of time integrators for quantum/classical molecular dynamics, in "Computational Molecular Dynamics: Challenges, Methods, Ideas" (P. Deuflhard et al., eds.), Springer Lecture Notes in Computational Science and Engineering, Vol. 4 (1999), 421-432.
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1998

• Christian Lubich, Alexander Ostermann, Hopf bifurcation of reaction-diffusion and Navier-Stokes equations under discretization, Numer. Math. 81 (1998), 53-84.
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• Marlis Hochbruck, Christian Lubich, and Hubert Selhofer, Exponential integrators for large systems of differential equations, SIAM J. Sci. Comp. 19 (1998), 1552-1574.
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• Karel in 't Hout, Christian Lubich, Periodic orbits of delay differential equations under discretization, BIT 38 (1998), 72-91.
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• Marlis Hochbruck, Christian Lubich, Error analysis of Krylov methods in a nutshell, SIAM J. Sci. Comput. 19 (1998), 695-701.
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1997

• Marlis Hochbruck, Further optimized look-ahead recurrences for adjacent rows in the Padé table and Toeplitz matrix factorizations. J. Comp. Appl. Math. 86 (1997), 219-236.
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• Marlis Hochbruck, Christian Lubich, On Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal. 34 (1997), 1911-1925.
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• Christian Engstler, Christian Lubich, MUR8: a multirate extension of the eighth-order Dormand-Prince method, Appl. Numer. Math. 25 (1997), 185-192, special issue Time Integrators.
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• Ernst Hairer, Christian Lubich, The life-span of backward error analysis for numerical integrators, Numer. Math. 76 (1997), 441-462.
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• Harry Yserentant, A particle model of compressible fluids,Numer. Math. 76 (1997), 111-142.
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• Harry Yserentant, A new class of particle methods,Numer. Math. 76 (1997), 87-109.
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• Christian Engstler, Christian Lubich, Multirate extrapolation methods for differential equations with different time scales, Computing 58 (1997), 173-185.
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1996

• Christian Lubich, Alexander Ostermann, Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: Nonsmooth-data error estimates and applications to long-time behaviour, Appl. Numer. Math. 22 (1996), 279-292, special issue Runge-Kutta Centennial.
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• Ch. Lubich, I.H. Sloan, V. Thome'e, Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term, Math. Comp. 65 (1996), 1-17.
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• Martin H. Gutknecht, Marlis Hochbruck, Optimized look-ahead recurrences for adjacent rows in the Padé table, BIT 36:2, pages 264-286, 1996.
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1995

• Martin H. Gutknecht, Marlis Hochbruck, The stability of inversion formulas for Toeplitz matrices, Linear Algebra and its Applications 223/224, pages 307-324, 1995.
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• Peter Leinen, Data Structures and Concepts for Adaptive Finite Element methods, Computing 55, 1995, pages 325-354.
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• Christian Lubich, Alexander Ostermann, Runge-Kutta approximation of quasi-linear parabolic equations, Math. Comp. 64 (1995), 601-627.
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• Christian Lubich, Alexander Ostermann, Linearly implicit time discretization of non-linear parabolic equations, IMA J. Numer. Anal. 15 (1995), 555-583.
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• Christian Lubich, Alexander Ostermann, Interior estimates for time discretizations of parabolic equations, Appl. Numer. Math. 18 (1995) 241-251.
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