Current research field

  • Numerics analysis
  • Numerical Solution of differential equations
  • Biomathematics

Publications

Books

  • (with M.Brokate, N.Henze, F.Hettlich, A.Meister, T.Sonar) Grundwissen Mathematikstudium, Höhere Analysis, Numerik und Stochastik, Springer Spektrum , 2016.
  • (with M.Brokate, N.Henze, F.Hettlich, A.Meister, T.Sonar) Arbeitsbuch Grundwissen Mathematikstudium, Höhere Analysis, Numerik und Stochastik (Aufgaben, Hinweise, Lösungen und Lösungswege) Springer Spektrum , 2016.


Biomathematics

  • Permanence in Lotka-Volterra equations: Linked prey-predator systems, Math.Biosci.82:165-191(1986).
  • Permanence of some four-species Lotka-Volterra systems, Dissertation, Universität Wien, 1987.
  • Permanence of some ecological systems with several predator and one prey species, J.Math.Biol.26:217-232(1988).
  • Permanence of some four-species prey-predator systems modelled by Lotka- Volterra dynamics, In: Mathematical Ecology, Proc.of the Autumn Course, World Scientific, Singapore, New Jersey, Hong Kong, p.643-658, 1988.
  • A two-prey, two-predator system, Proc.11th Int. Conf. Nonlin. Oscillations, J.Bolyai Mathmatical Soc., Budapest, p.840-843, 1987.
  • Two-predators feeding on two prey species: A result on permanence, Math.Biosci.96:1-32(1989).

Numerical Solutions of Stiff ODEs

  • (with W.Auzinger, R.Frank) Asymptotic error expansions for stiff differential equations: Applications, Computing 43,223-253(1990).
  • (with W.Auzinger, R.Frank) Error structures for stiff initial value problems, p.16-25 in Numerical Treatment of Differential Equations, ed.by K.Stremel, Proc.of the Fifth Seminar NUMDIFF-5 Halle 1989, Teubner-Texte zur Mathematik, Band 121, Leipzig 1991.
  • (with W.Auzinger, R.Frank) A note on convergence concepts for stiff problems, Computing 44,197-208(1990).
  • (with W.Auzinger, R.Frank) The state of the art in the convergence theory for stiff ODEs, Proceedings of the IMACS 1991, ed.by R. Vichnevetsky, J. J. H. Miller, Dublin, 1991.
  • (with W.Auzinger, R.Frank) An extension of B-convergence for Runge-Kutta methods, Appl.Num.Math., 9,91-109(1992).
  • (with W.Auzinger, R.Frank) Modern convergence theory for stiff initial value problems, J.of Comp.and Appl.Math, J.Comp.Appl. 45,5-16(1993).
  • (with W.Auzinger, R.Frank) Extending convergence theory for nonlinear stiff problems, Part I, BIT 36, vol.4, 635-652(1996).
  • (with W.Auzinger) Kreiss resolvent conditions and strengthened Cauchy-Schwarz inequalities, APNUM 18, 57-67(1995).
  • (with A.Eder) A normal form for multistep companion matrices and its relevance in the convergence theory for stiff problems, Report Nr. 122/97, Institut für Angewandte und Numerische Mathematik, TU Wien, 1997.
  • (with A.Eder) A normal form for multistep companion matrices and its relevance in the convergence theory for stiff problems, Mathematical Models and Methods in Applied Sciences, Vol.11,No.1,57-70(2001).
  • On the convergence of backward differentiation formulas for non-autonomous stiff initial value problems, BIT 41, vol.5, 1039-1048(2001).
  • Convergence of BDFs applied to nonlinear stiff initial value problems, PAMM 1, vol.1, 510-511(2002).
  • Linear multistep methods applied to stiff initial value problems - a survey, Mathematical and Computer Modelling, Volume 40, Issue 11-12, 1181-1192, 2004.
  • (with W.Auzinger, O.Koch) Canonical forms for companion matrices and applications, in preparation.

Parabolic Problems

  • (with A.Ostermann, M.Thalhammer) Stability of linear multistep methods and applications to nonlinear parabolic problems, Applied Num.Math, Vol.48,3-4, 389-407(2003).

Validated Solution of ODEs

  • (with G.F.Corliss) On implicit Taylor series methods, in Computer Arithmetic and Enclosure Methods, in: Computer Arithmetic and Enclosure Methods, Proc. of the Third International IMACS-GAMM Symposium on Computer Arithmetic and Scientific Computing (SCAN 91), ed.L.Atanassova, J.Herzberger, North Holland, Amsterdam-London-New York-Tokyo, 1992.
  • (with G.F.Corliss, A.Griewank, P.Henneberger, F.A.Potra, H.J.Stetter, High-order stiff ODE solvers via automatic differentiation and rational prediction, Tech. Report IOKOMO 0296, TU Dresden, 1996.
  • (with G.F.Corliss, A.Griewank, A.Henneberger, F.A.Potra, H.J.Stetter) High-order stiff ODE solvers via automatic differentiation and rational prediction, Lecture Notes in Comput.Sci, 1196, 114-125(1997).

Theoretical Analysis of Phase Transitions

  • (with M.Haluska, D.Havlik, W.Schranz) Acoustic phonon dispersion in single-crystal C60 , J.Phys.Condens.Matter, 11 1009(1999).