Index

Work areas

1. Stability of numerical methods for delay differential equations.
2. Computation of the joint spectral radius of a family of matrices.
3. Regularization of forward backward parabolic partial differential equations.
4. Stiff delay equations Scholarpedia introduction .

Main collaborations

• Group of computational mathematics
• Ernst Hairer

1. N. Guglielmi, Fabian Wirth and M. Zennaro, Complex polytope extremality results for families of matrices , SIAM Journal of Matrix Analysis and Applications, 27(3) (2005), 721--743.
2. N. Guglielmi, On the Newton iteration in the application of collocation methods to implicit delay equations, Applied Numerical Mathematics, 53(2--4) (2005), 281--297.
3. N. Guglielmi and Ch. Lubich, Numerical periodic orbits of neutral delay differential equations, Discrete and Continuous Dynamical Systems, 13(4) (2005), 1057--1067.
4. N. Guglielmi and M. Zennaro, Polytope norms and related algorithms for the computation of the joint spectral radius , Proceedings della ``44th IEEE Conference on Decision and Control and European Control Conference 2005'' (Sevilla), pp 3007--3012.
5. A. Bellen, N. Guglielmi and S. Maset, Numerical methods for delay models in biomathematics, in Integration of Complex Systems in Biomedicine, A. Quarteroni (editor), Springer Verlag (2006) in stampa.
6. N. Guglielmi, Open issues in devising software for the numerical solution of implicit delay differential equations, Journal of Computational and Applied Mathematics, 185(2) (2006), 261--277.
7. N. Guglielmi, Short proofs and a counterexample for analytical and numerical stability of delay equations with infinite memory, IMA Journal of Numerical Analysis, 26(1) (2006), 60--77.
8. N. Guglielmi and E. Hairer, Computing breaking points in implicit delay differential equations, Advances in Computational Mathematics, (in press, 2007).
9. G. Bellettini, G. Fusco and N. Guglielmi, A concept of solution for forward-backward equations, Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 16 (2006) 1--60.
10. N. Guglielmi and M. Zennaro, Balanced complex polytopes and related vector and matrix norms, Journal of Convex Analysis, 14 (2007) 729--766.
11. Y. Muroya, E. Ishiwata and N. Guglielmi, Global stability for nonlinear difference equations with variable coefficients, 334 (2007) 232--247.
12. N. Guglielmi e M. Zennaro, An algorithm for finding extremal polytope norms of matrix families, Linear Algebra and its Applications, {in press, 2007}.
13. N. Guglielmi and L. Hatvani, On small oscillations of dynamical systems with time-dependent kinetic and potential energy, Discrete and Continuous Dynamical Systems - Series A (DCDS-A), {in press, 2007}.
14. A. Bellen e N. Guglielmi, Solving neutral delay differential equations with state-dependent delays, Journal of Computational and Applied Mathematics, {in press, 2007}.
15. J. De Luca, N. Guglielmi e A.Politi, Electromagnetic two-body problem: recurrent dynamics in presence of state-dependent delays, 2007.
16. N. Guglielmi e M. Zennaro, Finding extremal complex polytope norms for families of real matrices,submitted to SIAM Journal of Matrix Analysis and Applications, 2008

    (the Matlab files for the computation of the complex polytope norms of the given Example may be downloaded here ).

• RETARD Extension of the code DOPRI5 to delay differential equations y'(t)=f(t,y(t),y(t-a),...)
• DR_RETARD Driver for RETARD

• the tar file radar5-v2.1.tar contains a directory with the Fortran 90 code RADAR5, the necessary linear algebra routines, and subdirectories for the following eleven examples. For unfolding the directory use the command tar xvf radar5-v2.1.tar
• ENZYME kinetics with an inhibitor molecule, dimension 4, one constant delay;
• HAYASHI an almost singular state dependent neutral problem, dimension 2 as differential-algebraic problem, one vanishing delay;
• HEPATITIS acute hepatitis B virus infection, dimension 10, 5 constant delays;
• OREGONATOR chemical kinetics, dimension 2, one constant delay;
• ROBERTSON chemical reaction with steady state solution, dimension 3, one constant delay, very large time interval (step sizes larger than the delay);
• SDISC, non smooth artificial problem, dimension 1, 1 constant delay;
• WALTMAN, threshold model for antibody production, dimension 6, 2 state-dependent delays tending to zero, discontinuities in the right-hand side of the equations;
• PAUL, state-dependent artificial problem, various order discontinuities;
• ELSNOR, problem with solution termination;
• MODCEG, neutral problem with state dependent delays and termination
• NEUTLOG, predator-pray neutral Gause-model.

Courses

1. Calculus and first course of Mathematics, undergraduate. Program . (faculty of Biotechnologies) .
2. Advanced numerical analysis (laurea magistralis in Mathematics) .
3. Elements of biomathematics. (laurea in Biotechnologies) Programma .
4. Laboratory of mathematics (laurea in Biotehcnologies) .

• NA-net (Numerical Analysts) home page NA-net
• Gruppo Nazionale per il Calcolo Scientifico GNCS
• Mathematical Review MathSciNet

Next conferences

• Recent acvances in functional and delay differential equations, Halifax, Canada, November 1 - 6, 2007. .
• Cnvegno Nazionale del GNCS, Montecatini, Italy, February 4 - 6, 2008. .
• AIMS' Seventh International Conference on Dyn. Systems, Diff. Equations and Applications, Arlington Texas, USA, May 18 - 21, 2008. .

Connections