RESEARCH PROJECT
Numerical Methods and Software for Differential Equations

TARGET: Numerical methods for stiff ODE-IVPs and ODE-BVPs



Papers:
  1. L.Brugnano, C.Magherini. Blended General Linear Methods based on Boundary Value Methods in the Generalized BDF family. Jour. Numer. Anal. Ind. Appl. Math. 4, 1-2 (2009) 23-40.
  2. F.Mazzia, A.Sestini. The BS class of Hermite spline quasi-interpolants on nonuniform knot distributions. BIT Numer. Math. 49 (2009) 611-628.
  3. L.Brugnano, F.Mazzia, D.Trigiante. Fifty Years of Stiffness. Annals of the European Academy of Sciences, 2009 (in press) arXiv:0910.3780.
  4. L.Brugnano, F.Mazzia, D.Trigiante. The role of the precise definition of stiffness in designing codes for the solution of ODEs. AIP Conf. Proc. 1168 (2009) 731-734.
  5. J.R.Cash, F.Mazzia. Efficient Global Methods for the Numerical Solution of Nonlinear Systems of Two point Boundary Value Problems. Annals of the European Academy of Sciences, 2009 (in press).
  6. P. Amodio, G. Settanni. Variable step/order generalized upwind methods for the numerical solution of second order singular perturbation problems. Journal of Numerical Analysis, Industrial and Applied Mathematics 4 (2009) 65-76.
  7. P. Amodio, G. Settanni. A deferred correction approach to the solution of singularly perturbed BVPs by high order upwind methods: implementation details. AIP Conference Proceedings 1168 (2009) 711-714. (doi: 10.1063/1.3241565)
  8. P. Amodio, G. Settanni. High order finite difference schemes for the solution of second order initial value problems. Journal of Numerical Analysis, Industrial and Applied Mathematics 5 (2010) 3-16.
  9. F.Mazzia, A.M.Nagy. Stiffness detection strategy for Explicit Runge Kutta Methods. AIP Conf. Proc. 1281 (2010) 239-242.
  10. L.Aceto, D.Trigiante. Special polynomials as continuous dynamical systems. Submitted.


Communications:
  1. L.Aceto. Pascal matrix and special polynomials.  Fourth workshop on Advanced Special Functions and solution of PDEs (4th ASP 2009 ), Sabaudia (Latina), 24-28 Maggio 2009.
  2. F.Mazzia. The role of the precise definition of stiffness in designing codes for the solution of ODEs. ICAANM 2009, Crete (Greece) September 18-22, 2009.
  3. P.Amodio. On the solution of second order singular perturbation problems by generalized upwind methods. ICNAAM 2009, Crete (Greece) September 18-22, 2009.
  4. F.Mazzia. Conditioning and Hybrid Mesh Selection Algorithms for Two-Point Boundary Value Problems. BIT 50 (invited).  (abstract on page 79 of the program).
  5. F.Mazzia. Fifty Years of Stiffness. ICCAM 2010, Leuven (B), July 5-9, 2010 (plenary lecture).    (abstract)
  6. F.Mazzia. Stifness detection strategy for explicit Runge-Kutta methods. ICNAAM 2010, Rodhes (Greece) September 19-25, 2010.