Arbeiten Papers

Bernhard A. Schmitt

• Lang, J; Schmitt, B.A (2022)
  Discrete adjoint implicit peer methods in optimal control
  J.Comput.Appl.Math. 416, 114596
• 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
• 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
• 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".
• 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
• 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,
• Schmitt, B.A. (2014)
  Algebraic criteria for A-stability of peer two-step methods
  Bericht 2014-05, Marburg; arXiv:1506.05738
• 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.
• 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
• 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.
• 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.
• 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)
• 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
• 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.
• 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
• 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
• Weiner, R.; Schmitt, B.A.; Podhaisky, H.; Jebens, S. (2009)
  Superconvergent explicit two-step peer methods
  J. Comput. Appl. Math. 223, 753-764.
• 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
• 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
• 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.
• Weiner, R.; Jebens, S.; Schmitt, B.A.; Podhaisky, H.(2006)
  Explicit parallel two-step peer methods
  Report 10 (2006), Inst. of Numerical Math., Halle.
• 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.
• 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.
• 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
• Podhaisky,H.; Weiner,R.; Schmitt,B.A. (2005)
  Rosenbrock-type 'peer' two-step methods,
  Appl. Numer. Math. 53, 409-420.
• 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.
• 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).
• Podhaisky,H.; Weiner,R; Schmitt,B.A. (2002)
  Two-step W-methods for stiff ODE systems.
  Vietnam J. Math. 30, 591-603.
  Report, Halle.
• 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
• 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.
• Schmitt,B.A.; Weiner,R. (2001)
  Equilibrium attractivity of Runge-Kutta methods.
  IMA Journal on Numerical Analysis 21, 327-348.
• 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.
• Podhaisky,H.; Schmitt,B.A.; Weiner,R. (1999)
  Two-step W-methods with parallel stages.
  Report No. 22, Comp. Science&Scient. Computing, Halle,
• Weiner,R.; Schmitt,B.A. (1998)
  Order results for Krylov-W-methods.
  Computing 61, 69-89
• Schmitt,B.A.; Weiner,R. (1998)
  Polynomial preconditioning in Krylov-ROW methods.
  Appl. Numer. Math. 28, 427-437;
• Schmitt,B.A.; Weiner,R. (1998)
  Equilibrium attractivity of Krylov-W-methods for nonlinear stiff ODEs.
  BIT 38, 391-414.
• Podhaisky,H.; Weiner,R.; Schmitt,B.A. (1998)
  Numerical experiments with Krylov integrators.
  Appl. Numer. Math. 28, 413-425.
• 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.)
• Schmitt,B.A.; Weiner,R. (1995)
  Matrix-free W-methods using a multiple Arnoldi iteration.
  Appl. Numer. Math. 18, 307-320.
• 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.
• Schmitt,B.A.; Mei Zhen. (1993)
  Construction of higher order algebraic one-step schemes in stiff BVPs.
  Appl. Numer. Math. 13, 199-208.
• Büttner,M.; Schmitt,B.A.; Weiner,R. (1993)
  Automatic partitioning in linearly-implicit Runge-Kutta methods.
  Appl. Numer. Math. 13, 41-55.
• Schmitt,B.A. (1992)
  Perturbation bounds for matrix square roots and Pythagorean sums.
  Linear Algebra Applcs. 174, 215-227.
• Schmitt,B.A. (1992)
  Krylov approximations for matrix square roots in stiff boundary value problems.
  Math. Comp. 58, 191-212.
• 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
• 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
• Schmitt,B.A. (1990)
  An algebraic approximation for the matrix exponential in singularly perturbed boundary value problems.
  SIAM J. Numer. Anal. 27, 51-66.
• Schmitt,B.A. (1988)
  Stability of implicit Runge-Kutta methods for nonlinear stiff differential equations.
  BIT 28, 884-897.
• 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.
• Böhmer,K.; Gross,W; Schmitt,B.A.; Schwarz,R (1984)
  Defect corrections and Hartree-Fock methods.
  Defect correction methods, Computing Suppl. 5. 193-209.
• Schmitt,B.A. (1983)
  Norm bounds for rational matrix functions.
  Numer. Math. 42, 379-389