Numerical Analysis Group


versione italiana

Members

  1. Alfredo Bellen
  2. Marino Zennaro
  3. Igor Moret
  4. Rossana Vermiglio
  5. Lucio Torelli
  6. Stefano Maset
  7. Nicola Guglielmi
  8. Paolo Novati
  9. Dimitri Breda

Current interest and research areas

  • Numerical methods for ordinary and functional differential equations (in particular, delay equations).
  • Numerical solution of delay differential equations as abstract Cauchy problems.
  • Computation of the spectral radius of a family of matrices with applications to the study of stability of difference equations (in particular, those obtained from stability problems for numerical methods for differential equations).
  • Development of codes for delay differential equations.
  • Krylov subspace methods for the approximation of matrix functions with applications to the numerical solutions of large scale differential problems.

 

List of publications of the Group

 

numerical codes


Delay differential equations

For nonstiff problems:

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

For stiff problems, including differential-algebraic problems, neutral problems and, in general, equations with constant or state-dependent delays (possibly vanishing):

  • the tar file radar5.tar contains a directory with the code RADAR5, written in Fortran 90, the necessary routines of linear algebra and some sub-directories containing the following seven examples:
  1. ENZYME: kinetics of an enzyme with an inhibitory molecule, dimension 4, one constant delay;
  2. HAYASHI: neutral quasi-singular problem, dimension 2 as a differential-algebraic problem, one vanishing state-dependent delay;
  3. HEPATITIS: acute viral infection (hepatitis B), dimension 10, five constant delays;
  4. OREGONATOR: chemical kinetics, dimension 2, one constant delay;
  5. ROBERTSON: chemical reaction with stationary solution, dimension 3, one constant delay, very long integration interval (using stepsizes larger than the delay);
  6. SDISC: artificial problem with non-smooth solution, dimension 1, one constant delay;
  7. WALTMAN: threshold model for the reproduction of antibodies, dimension 6, two asymptotically vanishing state-dependent delays, discontinuities in the right-hand side of the equation.

To create directories and files, use the command tar xvf radar5.tar

 

Summer Schools in Dobbiaco (BZ), Italy

·         Numerical Methods for ODEs (July 3 - 7, 2000)

·         Time Delay Equations and Control Theory (June 25 - 29, 2001)

·         Numerical Treatment of Dynamical Systems (June 17 - 21, 2002)

·         Numerical Methods for Evolution Equations (June 28 - July 2, 2004)

·         Mathematical Models in Life Sciences: Theory and Simulation (July 1 - 5, 2005)

·         Delay Differential Equations and Applications (June 26 - 30, 2006)