Arbeiten Papers
Bernhard A. Schmitt
- Lang, J.; Schmitt, B.A.; (2024)
Variable-stepsize implicit Peer triplets in ODE constrained optimal control
arXiv:2404.13716
- Lang, J.; Schmitt, B.A.; (2023)
Implicit Peer triplets in gradient-based solution algorithms for ODE constrained optimal control
arXiv:2303.18180
- Lang, J.; Schmitt, B.A.; (2023)
Exact discrete solutions of boundary control problems for the 1D heat equation
J. Optim. Theory Appl. 196, 1106-1118, doi:10.1007/s10957-022-02154-4
- Lang, J.; Schmitt, B.A.; (2022)
Implicit A-stable peer triplets for ODE constrained optimal control problems
Algorithms 2022, 15, 310,
doi:10.3390/a15090310
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Lang, J; Schmitt, B.A (2022)
Discrete adjoint implicit peer methods in optimal control
J.Comput.Appl.Math. 416, 114596, doi:10.1016/j.cam.2022.114596
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Winkler, J; Denhard, M; Schmitt, B.A (2020)
Krylov Methods for Adjoint-Free Singular Vector Based Perturbations in Dynamical Systems
Q J R Meteorol Soc. 2020;146:225-239
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Schenk, K; Hervas, A: Rösch, T; Eisemann, M; Schmitt, B.A; Dahlke, S; Kleine-Borgmann, L; Murray, S.M; Graumann P.(2017)
Rapid turnover of DnaA at replication origin regions contributes to initiation control of DNA replication
PLOS Genetics 13(2): e1006561
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Schmitt, B.A. (2016)
Data sets for verification of A-stability and zero stability of peer two-step methods,
Mendeley Data, v1 http://dx.doi.org/10.17632/7393kvzn33.1
The data set contains Maxima worksheets and PDF output with additional data and the computations
for verification of the algebraic criteria for A- and zero stability of the 4 new peer methods from
the paper "Efficient A-stable peer two-step methods".
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Schmitt, B.A.; Weiner, R. (2016)
Efficient A-stable peer two-step methods,
J. Comput. Appl. Math. 316, 319-329, doi:10.1016/j.cam.2016.08.045
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Rashkov,P; Schmitt, B.A.; Keilberg,D.; Beck, K.; Sogaard-Andersen, L.; Dahlke, S. (2014)
A model for spatio-temporal dynamics in a regulatory network for cell polarity,
Mathematical Biosciences 258, 189-200, ISSN 0025-5564,
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Schmitt, B.A. (2014)
Algebraic criteria for A-stability of peer two-step methods
Bericht 2014-05, Marburg; arXiv:1506.05738
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Rashkov,P; Schmitt, B.A.; Sogaard-Andersen, L.; Lenz, P.; Dahlke, S. (2013)
A model for antagonistic protein dynamics.
Intern. J. Biomathematics and Biostatistics, Vol. 2, 75-85.
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Schmitt, B.A. (2014)
Peer methods with improved embedded sensitivities for parameter-dependent ODEs
J. Comput. Appl. Math. 256, 242-253.
Preprint: Bericht 2013-01, Marburg
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Schmitt, B.A.; Weiner, R.; Beck, S. (2013)
Two-step peer methods with continuous output,
BIT Numerical Mathematics 53, 717-739.
Preprint:
Bericht Nr.2012-02, Marburg.
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Böhmer, K; Schild, K.H.; Schmitt, B.A. (2013)
Dew drops on spider webs: a symmetry breaking bifurcation for a parabolic differential-algebraic equation
J. Comput. Appl. Math. 254, 99-115.
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Schmitt, B.A; Kostina, E. (2012)
Peer two-step methods with embedded sensitivity approximation for parameter-dependent ODEs,
SIAM J. Numer. Anal. 50, 2182-2207.
(PDF here)
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Rashkov, P.; Schmitt, B.A.; Sogaard-Anderesen, L.; Lenz, P.; Dahlke, S. (2012)
A model of oscillatory protein dynamics in bacteria
Bull. Math. Biol. 74:2183-2203, DOI 10.1007/s11538-012-9752-y
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Beck, S.; Weiner, R.; Podhaisky, H.; Schmitt, B.A. (2012)
Implicit peer methods for large stiff ODE systems,
J. Appl. Math. Comp. 38, 389-406.
Preprint: Report 07 (2010), Institut für Mathematik, Halle.
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Schmitt, B.A. (2012)
On algebraic stability of general linear methods and peer methods
Appl. Numer. Math. 62, 1544-1553
Preprint: Bericht Nr.2009-04, Marburg
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Schmitt, B.A.; Weiner, R. (2010)
Parallel start for explicit parallel two-step peer methods
Numer. Algor. 53, 363-381.
Preprint: Bericht Nr.2008-8, Marburg
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Weiner, R.; Schmitt, B.A.; Podhaisky, H.; Jebens, S. (2009)
Superconvergent explicit two-step peer methods
J. Comput. Appl. Math. 223, 753-764.
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Schmitt, B.A.; Weiner, R.; Jebens, S. (2009)
Parameter optimization for explicit parallel peer two-step methods
Appl. Numer. Math. 59, 769-782.
Preprint: Bericht Nr.2006-7
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Jebens, S.; Weiner, R.; Podhaisky, H.; Schmitt, B.A. (2008)
Explicit multi-step peer methods for special second order differential equations
Appl. Math. Comput. 202, 803-813.
Preprint:
Report 19 (2007), Halle
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Weiner, R.; Biermann, K.; Schmitt, B.A.; Podhaisky, H. (2008)
Explicit two-step peer methods
Comput. Math.Applcs 55, 609-619
Preprint: Report 10 (2005), Halle.
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Weiner, R.; Jebens, S.; Schmitt, B.A.; Podhaisky, H.(2006)
Explicit parallel two-step peer methods
Report 10 (2006), Inst. of Numerical Math., Halle.
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Podhaisky, H.; Weiner, R.; Schmitt, B.A. (2006)
Linearly-implicit two-step methods and their implementation in Nordsieck-form ,
Appl. Numer. Math. 56, 374-387.
Preprint: Report 25 (2004), Halle.
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Schmitt,B.A.; Weiner,R.; Podhaisky,H. (2005)
Multi-implicit peer two-step W-methods for parallel time integration,
BIT 45, 197-217.
Preprint: Bericht 2004-4.
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Schmitt,B.A; Weiner,R; Erdmann,K. (2005)
Implicit parallel peer methods for stiff initial value problems,
Appl. Numer. Math. 53, 457-470.
Preprint: Report 2003-7
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Podhaisky,H.; Weiner,R.; Schmitt,B.A. (2005)
Rosenbrock-type 'peer' two-step methods,
Appl. Numer. Math. 53, 409-420.
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Schmitt,B.A.; Weiner,R.; Podhaisky,H. (2004)
Parallel 'Peer' two-step W-methods and their application to MOL-systems.
Appl. Numer. Math. 48, 425-439.
Preprint: Report 02 (2003), Halle.
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Schmitt,B.A.; Weiner,R. (2004)
Parallel Two-Step W-Methods with Peer Variables,
SIAM J. Numer. Anal. 42, 265-282;
Preprint: Report 92 (2002).
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Podhaisky,H.; Weiner,R; Schmitt,B.A. (2002)
Two-step W-methods for stiff ODE systems.
Vietnam J. Math. 30, 591-603.
Report, Halle.
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Podhaisky,H.; Schmitt,B.A.; Weiner,R. (2002)
Design, analysis and testing of some parallel two-step W-methods for stiff systems.
Appl. Numer. Math. 42, 381-395
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Weiner,R.; Schmitt,B.A.; Podhaisky,H. (2001)
Parallel two-step W-methods on singular perturbation problems.
Springer Lecture Notes in Computer Science 2328, 778-785.
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Schmitt,B.A.; Weiner,R. (2001)
Equilibrium attractivity of Runge-Kutta methods.
IMA Journal on Numerical Analysis 21, 327-348.
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Weiner,R.; Schmitt,B.A.; Podhaisky,H. (2000)
Two-step W-methods on singular perturbation problems.
FB Mathematik u. Informatik, Uni Marburg, Bericht 73, 14 S.
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Podhaisky,H.; Schmitt,B.A.; Weiner,R. (1999)
Two-step W-methods with parallel stages.
Report No. 22, Comp. Science&Scient. Computing, Halle,
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Weiner,R.; Schmitt,B.A. (1998)
Order results for Krylov-W-methods.
Computing 61, 69-89
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Schmitt,B.A.; Weiner,R. (1998)
Polynomial preconditioning in Krylov-ROW methods.
Appl. Numer. Math. 28, 427-437;
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Schmitt,B.A.; Weiner,R. (1998)
Equilibrium attractivity of Krylov-W-methods for nonlinear stiff ODEs.
BIT 38, 391-414.
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Podhaisky,H.; Weiner,R.; Schmitt,B.A. (1998)
Numerical experiments with Krylov integrators.
Appl. Numer. Math. 28, 413-425.
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Weiner,R.; Schmitt,B.A.; Podhaisky,H. (1997)
ROWMAP - a ROW code with Krylov techniques for large stiff ODEs.
Appl. Numer. Math. 25, 303-319 (Innov.time integr.)
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Schmitt,B.A.; Weiner,R. (1995)
Matrix-free W-methods using a multiple Arnoldi iteration.
Appl. Numer. Math. 18, 307-320.
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Büttner,M.; Schmitt,B.A.; Weiner,R. (1995)
W-methods with automatic partitioning by Krylov techniques for large stiff systems.
SIAM J. Numer. Anal. 32, 260-284.
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Schmitt,B.A.; Mei Zhen. (1993)
Construction of higher order algebraic one-step schemes in stiff BVPs.
Appl. Numer. Math. 13, 199-208.
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Büttner,M.; Schmitt,B.A.; Weiner,R. (1993)
Automatic partitioning in linearly-implicit Runge-Kutta methods.
Appl. Numer. Math. 13, 41-55.
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Schmitt,B.A. (1992)
Perturbation bounds for matrix square roots and Pythagorean sums.
Linear Algebra Applcs. 174, 215-227.
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Schmitt,B.A. (1992)
Krylov approximations for matrix square roots in stiff boundary value problems.
Math. Comp. 58, 191-212.
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Schmitt,B.A. (1992)
On the implementation of an algebraic difference scheme for stiff BVPs.
Computational ordinary differential equations, IMA Conference on Computational ODEs, London '89, Eds. J.R.Cash, I.Gladwell; 457 S.. 193-200
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Schmitt,B.A.; Schild,K.H. (1991)
Error estimation and mesh adaptation for an algebraic difference scheme in stiff BVPs.
NUMDIFF-5, Numerical treatment of DEs, Halle'89. p. 152-161
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Schmitt,B.A. (1990)
An algebraic approximation for the matrix exponential in singularly perturbed boundary value problems.
SIAM J. Numer. Anal. 27, 51-66.
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Schmitt,B.A. (1988)
Stability of implicit Runge-Kutta methods for nonlinear stiff differential equations.
BIT 28, 884-897.
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Böhmer,K.; Schmitt,B.A. (1988)
Highly accurate solutions of the Hartree-Fock equations via defect corrections.
NUMDIFF-4, Numerical Treatment of DEs, Halle'87. Ed.. 289-294.
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Böhmer,K.; Gross,W; Schmitt,B.A.; Schwarz,R (1984)
Defect corrections and Hartree-Fock methods.
Defect correction methods, Computing Suppl. 5. 193-209.
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Schmitt,B.A. (1983)
Norm bounds for rational matrix functions.
Numer. Math. 42, 379-389