RESEARCH PROJECT
Numerical Methods and Software for Differential Equations

TARGET: Numerical methods for Hamiltonian problems



Papers:
  1. L.Brugnano, D.Trigiante. Energy drift in the numerical integration of Hamiltonian problems. Jour. Numer. Anal. Ind. Appl. Math. 4,3-4 (2009) 153-170.
  2. F.Iavernaro, D.Trigiante. High-order symmetric schemes for the energy conservation of polynomial Hamiltonian problems. Jour. Numer. Anal. Ind. Appl. Math. 4,1-2 (2009) 87–111.
  3. L.Aceto, D.Trigiante. On the periodic solutions of discrete Hamiltonian systems. AIP Conf. Proc. 1168 (2009) 707-710.
  4. L.Brugnano, F.Iavernaro, D.Trigiante. Hamiltonian BVMs (HBVMs): a family of “drift free” methods for integrating polynomial Hamiltonian problems. AIP Conf. Proc. 1168 (2009) 715-718.
  5. L.Brugnano, F.Iavernaro, T.Susca. Hamiltonian BVMs (HBVMs): implementation details and applications. AIP Conf. Proc. 1168 (2009) 723-726.
  6. L.Brugnano, F.Iavernaro, D.Trigiante. Analysis of Hamiltonian Boundary Value Methods (HBVMs) for the numerical solution of polynomial Hamiltonian dynamical systems. (2009) submitted  arXiv:0909.5659.
  7. L.Brugnano, F.Iavernaro, D.Trigiante. Hamiltonian Boundary Value Methods (Energy Preserving Discrete Line Integral Methods). Jour. Numer. Anal. Ind. Appl. Math. 5,1-2 (2010) 17-37 arXiv:0910.3621.
  8. L.Brugnano, F.Iavernaro, D.Trigiante. Isospectral Property of Hamiltonian Boundary Value Methods (HBVMs) and their blended implementation. (2010) submitted  arXiv:1002.1387.
  9. L.Brugnano, F.Iavernaro, T.Susca. Numerical comparisons between Gauss-Legendre methods and Hamiltonian BVMs defined over Gauss points. Monografias de la Real Acedemia de Ciencias de Zaragoza (Special Issue devoted to the 65th birthday of Manuel Calvo), (2010) in press.  arXiv:1002.2727.
  10. L.Brugnano, F.Iavernaro, D.Trigiante. The Hamiltonian BVMs (HBVMs) Homepage. arXiv:11002.2757.
  11. L.Brugnano, F.Iavernaro, D.Trigiante. Isospectral Property of Hamiltonian Boundary Value Methods (HBVMs) and their connections with Runge-Kutta collocation methods. arXiv:1002.4394.
  12. L.Brugnano, F.Iavernaro, D.Trigiante. On the Existence of Energy-Preserving Symplectic Integrators Based upon Gauss Collocation Formulae. arXiv:1005.1930.
  13. L.Brugnano, F.Iavernaro, D.Trigiante. Energy and quadratic invariants preserving integrators of Gaussian type. AIP Conf. Proc. 1281 (2010) 227-230. arXiv:1008.4790.
  14. L.Brugnano, F.Iavernaro, D.Trigiante. Numerical comparisons among some methods for Hamiltonian problems . AIP Conf. Proc. 1281 (2010) 214-218. arXiv:1008.4791.
  15. L.Brugnano, F.Iavernaro, D.Trigiante. Numerical Solution of ODEs and the Columbus' Egg: Three Simple Ideas for Three Difficult Problems. Mathematics in Engineering, Science and Aerospace.  1, 4  (2010) 407-426. arXiv:1008.4789.
  16. L.Brugnano, F.Iavernaro, D.Trigiante. A unifying approach for the derivation and analysis of effective classes of one-step methods for ODEs. Preprint (2010). arXiv:1009.3165. 
  17. L.Brugnano, F.Iavernaro, D.Trigiante. The Lack of Continuity and the Role of Infinite and Infinitesimal in Numerical Methods: the Case of Symplecticity in Collocation Methods.  Applied Mathematics and Computation (accepted) arXiv:1010.4538.
  18. L.Brugnano, F.Iavernaro, D.Trigiante. A note on the efficient implementation of Hamiltonian BVMs. Jour. Comput. Appl. Math. (to appear) arXiv:1012.2323.
  19. L.Brugnano, F.Iavernaro, D.Trigiante. A Two Step, Fourth Order, Nearly-Linear Method with Energy Preserving Properties. (2011) arXiv:1106.0598.



Communications:
  1. L.Brugnano. Hamiltonian Boundary Value Methods (HBVMs) for the numerical solution of polynomial Hamiltonian dynamical systems (plenary lecture). International Conference "MCalv6(5)", Zaragoza (Spain) September 7-8, 2009.
  2. L.Aceto. On the periodic solutions of discrete Hamiltonian systems. ICNAAM 2009, Crete (Greece) September 18-22, 2009.
  3. L.Brugnano. Hamiltonian BVMs (HBVMs): a family of "drift free" methods for integrating polynomial Hamiltonian  problems. ICNAAM 2009, Crete (Greece) September 18-22, 2009.
  4. F.Iavernaro. Hamiltonian BVMs (HBVMs): implementation details and applications. ICNAAM 2009, Crete (Greece) September 18-22, 2009.
  5. L.Brugnano. Numerical comparisons among some methods for Hamiltonian problems. ICNAAM 2010, Rhodes (Greece) September 19-25, 2010.
  6. F.Iavernaro. Energy and quadratic invariants preserving integrators of Gaussian type. ICNAAM 2010, Rhodes (Greece) September 19-25, 2010.
 
Links:     The HBVMs Homepage