Research
Bücher
- (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).
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