Publications

  1. F. Scarabel, O. Diekmann and R. Vermiglio, Numerical bifurcation analysis of renewal equations via pseudospectral approximation, submitted, arXiv: 2012.05364 [math.NA], 2020.
  2. A. Andò, D. Breda, D. Liessi, S. Maset, F. Scarabel and R. Vermiglio, 15 years or so of pseudospectral collocation methods for stability and bifurcation of delay equations, in series Adv. Delays Dyn., Springer, to appear.
  3. R. Vermiglio and A. Zamolo, Sensitivity analysis for stability of uncertain delay differential equations using polynomial chaos expansions, in series Adv. Delays Dyn., Springer, to appear.
  4. D. Breda, F. Florian, J. Ripoll and R. Vermiglio, Efficient numerical computation of the basic reproduction number for structured populations, J. Comput. Appl. Math., 384 (2021), 113165, DOI: 10.1016/j.cam.2020.113165.
  5. D. Breda, T. Kuniya, J. Ripoll and R. Vermiglio, Collocation of next-generation operators for computing the basic reproduction number of structured populations, J. Sci. Comput., 85 (2020), 40, DOI: 10.1007/s10915-020-01339-1.
  6. O. Diekmann, F. Scarabel and R. Vermiglio, Pseudospectral discretization of delay differential equations in sun-star formulation: Results and conjectures, Discrete Contin. Dyn. Syst. Ser. S, 13 (2020), pp. 2575–2602, DOI: 10.3934/dcdss.2020196.
  7. F. Florian and R. Vermiglio, PC-based sensitivity analysis of the basic reproduction number of population and epidemic models, in M. Aguiar, C. Braumann, B. W. Kooi, A. Pugliese, N. Stollenwerk and E. Venturino, eds., Current Trends in Dynamical Systems in Biology and Natural Sciences, SEMA SIMAI Springer Ser. 21, Springer, Cham, 2020, pp. 205–222, DOI: 10.1007/978-3-030-41120-6_11.
  8. F. Scarabel, D. Breda, O. Diekmann, M. Gyllenberg and R. Vermiglio, Numerical bifurcation analysis of physiologically structured population models via pseudospectral approximation, Vietnam J. Math. (2020), DOI: 10.1007/s10013-020-00421-3.
  9. M. Gyllenberg, F. Scarabel and R. Vermiglio, Equations with infinite delay: Numerical bifurcation analysis via pseudospectral discretization, Appl. Math. Comput., 333 (2018), pp. 490–505, DOI: 10.1016/j.amc.2018.03.104.
  10. R. Vermiglio, Polynomial chaos expansions for the stability analysis of uncertain delay differential equations, SIAM/ASA J. Uncert. Quant., 5 (2017), pp. 278–303, DOI: 10.1137/15M1029618.
  11. D. Breda, O. Diekmann, M. Gyllenberg, F. Scarabel and R. Vermiglio, Pseudospectral discretization of nonlinear delay equations: New prospects for numerical bifurcation analysis, SIAM J. Appl. Dyn. Syst., 15 (2016), pp. 1–23, DOI: 10.1137/15M1040931.
  12. R. Vermiglio, Numerical approximation of the non-essential spectrum of abstract delay differential equations, Math. Comput. Simulat., 125 (2016), pp. 56–69, DOI: 10.1016/j.matcom.2015.10.009.
  13. D. Breda, S. Maset and R. Vermiglio, Stability of Linear Delay Differential Equations: A Numerical Approach with MATLAB, SpringerBriefs Control Autom. Robot., Springer, New York, 2015, DOI: 10.1007/978-1-4939-2107-2.
  14. D. Breda, P. Getto, J. Sánchez Sanz and R. Vermiglio, Computing the eigenvalues of realistic Daphnia models by pseudospectral methods, SIAM J. Sci. Comput., 37 (2015), A2607-A2629, DOI: 10.1137/15M1016710.
  15. L. Contento, A. Ern and R. Vermiglio, A linear-time approximate convex envelope algorithm using the double Legendre–Fenchel transform with application to phase separation, Comput. Ottim. Appl., 60 (2015), pp. 231–261, DOI: 10.1007/s10589-014-9666-8.
  16. D. Breda, S. Maset and R. Vermiglio, Pseudospectral methods for stability analysis of delayed dynamical systems, Int. J. Dyn. Control, 2 (2014), pp. 143–153, DOI: 10.1007/s40435-013-0041-x.
  17. D. Breda, O. Diekmann, S. Maset and R. Vermiglio, A numerical approach for investigating the stability of equilibria for structured population models, J. Biol. Dyn., 7 (2013), pp. 4–20, DOI: 10.1080/17513758.2013.789562.
  18. D. Breda, S. Maset and R. Vermiglio, Approximation of eigenvalues of evolution operators for linear retarded functional differential equations, SIAM J. Numer. Anal., 50 (2012), pp. 1456–1483, DOI: 10.1137/100815505.
  19. D. Breda, S. Maset and R. Vermiglio, Numerical recipes for investigating endemic equilibria of age-structured SIR epidemics, Discrete Contin. Dyn. Syst., 32 (2012), pp. 2675–2699, DOI: 10.3934/dcds.2012.32.2675.
  20. D. Breda, O. Diekmann, W. F. de Graaf, A . Pugliese and R. Vermiglio, On the formulation of epidemic models (an appraisal of Kermack and McKendrick), J. Biol. Dyn., 6 (2012), pp. 103–117, DOI: 10.1080/17513758.2012.716454.
  21. D. Breda, D. Esseni, A. Paussa, R. Specogna, F. Trevisan and R. Vermiglio, Comparison between pseudospectral and discrete geometric methods for modelling quantization effects in nanoscale electron devices, IEEE Trans. Magn., 48 (2012), pp. 203–206, DOI: 10.1109/TMAG.2011.2174142.
  22. D. Breda, S. Maset and R. Vermiglio, Discretization of solution operators for linear time invariant – time delay systems in Hilbert spaces, in R. Sipahi, T. Vyhlídal, S.-I. Niculescu and P. Pepe, eds., Time Delay Systems: Methods, Applications and New Trends, Lec. Notes Control Inf. Sci. 423, Springer, 2012, DOI: 10.1007/978-3-642-25221-1_16.
  23. D. Breda, S. Maset and R. Vermiglio, Computing eigenvalues of Gurtin–MacCamy models with diffusion, IMA J. Numer. Anal., 32 (2012), pp. 1030–1050, DOI: 10.1093/imanum/drr004.
  24. D. Breda, D. Esseni, A. Paussa, R. Specogna, F. Trevisan and R. Vermiglio, Comparison between pseudospectral and discrete geometric methods for modelling quantization effects in nanoscale electron devices, in Proceedings of the 18th International Conference on the Computation of Electromagnetic Fields (COMPUMAG2011), 2011.
  25. I. Mazzer and R. Vermiglio, An age-structured population dynamics model for several species with finite life-span, Research report, DIMI, University of Udine (2011), pp. 1–20.
  26. D. Breda, S. Maset and R. Vermiglio, Computation of asymptotic stability for a class of partial differential equations with delay, J. Vib. Control, 16 (2010), pp. 1005–1022, DOI: 10.1177/1077546309341106.
  27. D. Breda, S. Maset and R. Vermiglio, On discretizing the semigroup of solution operators for linear time invariant – time delay systems, in T. Vyhlídal and P. Zítek, eds., 9th IFAC Workshop on Time Delay Systems, IFAC Proceedings Volumes 43, Elsevier, 2010, DOI: 10.3182/20100607-3-cz-4010.00015.
  28. A. Paussa, F. Conzatti, D. Breda, R. Vermiglio, D. Esseni and P. Palestri, Pseudo-spectral methods for the modelling of quantization effects in nanoscale MOS transistors, IEEE Trans. Electron Devices, 57 (2010), pp. 3239–3249, DOI: 10.1109/TED.2010.2081673.
  29. A. Paussa, F. Conzatti, D. Breda, R. Vermiglio and D. Esseni, Pseudo-spectral methods for the modelling of quantization effects in nanoscale MOS transistors, in 2010 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD 2010), IEEE, 2010, pp. 299–302, DOI: 10.1109/SISPAD.2010.5604499.
  30. D. Breda, S. Maset and R. Vermiglio, An adaptive algorithm for efficient computation of level curves of surfaces, Numer. Algorithms, 52 (2009), pp. 605–628, DOI: 10.1007/s11075-009-9303-2.
  31. D. Breda, S. Maset and R. Vermiglio, Numerical approximation of characteristic values of partial retarded functional differential equations, Numer. Math., 113 (2009), pp. 181–242, DOI: 10.1007/s00211-009-0233-7.
  32. D. Breda, S. Maset and R. Vermiglio, TRACE-DDE: a Tool for Robust Analysis and Characteristic Equations for Delay Differential Equations, in J. J. Loiseau, W. Michiels, S.-I. Niculescu and R. Sipahi, eds., Topics in Time Delay Systems: Analysis, Algorithms, and Control, Lect. Notes Control Inf. Sci. 388, Springer, 2009, pp. 145–155, DOI: 10.1007/978-3-642-02897-7_13.
  33. D. Breda, M. Iannelli, S. Maset and R. Vermiglio, Stability analysis of the Gurtin–MacCamy model, SIAM J. Numer. Anal., 46 (2008), pp. 980–995, DOI: 10.1137/070685658.
  34. D. Breda, S. Maset and R. Vermiglio, Computing the characteristic values of partial retarded functional differential equations, in Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007, Proceedings in Applied Mathematics and Mechanics 7, 2007, pp. 1020405–1020406, DOI: 10.1002/pamm.200700648.
  35. D. Breda, C. Cusulin, M. Iannelli, S. Maset and R. Vermiglio, Stability analysis of age-structured population equations by pseudospectral differencing methods, J. Math. Biol., 54 (2007), pp. 701–720, DOI: 10.1007/s00285-006-0064-4.
  36. D. Breda, S. Maset and R. Vermiglio, Pseudospectral approximation of eigenvalues of derivative operators with non-local boundary conditions, Appl. Numer. Math., 56 (2006), pp. 318–331, DOI: 10.1016/j.apnum.2005.04.011.
  37. D. Breda, S. Maset and R. Vermiglio, Numerical computation of characteristic multipliers for linear time periodic delay differential equations, in C. Manes and P. Pepe, eds., 6th Workshop on Time Delay Systems, IFAC Proceedings Volumes 39, Elsevier, 2006, pp. 163–168, DOI: 10.3182/20060710-3-IT-4901.00027.
  38. D. Breda, S. Maset and R. Vermiglio, Pseudospectral differencing methods for characteristic roots of delay differential equations, SIAM J. Sci. Comput., 27 (2005), pp. 482–495, DOI: 10.1137/030601600.
  39. S. Maset, L. Torelli and R. Vermiglio, Runge–Kutta methods for retarded functional differential equations, Math. Models Comput. Simul., 15 (2005), pp. 1203–1251, DOI: 10.1142/S0218202505000716.
  40. D. Breda, S. Maset and R. Vermiglio, Efficient computation of stability charts for linear time delay systems, in Proceedings of the ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, ASME, 2005, pp. 857–866, DOI: 10.1115/DETC2005-84973.
  41. D. Breda, S. Maset and R. Vermiglio, Pseudospectral techniques for stability computation of linear time delay systems, in Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference, IEEE, 2005, DOI: 10.1109/CDC.2005.1582352.
  42. D. Breda, S. Maset and R. Vermiglio, Computing the characteristic roots for delay differential equations, IMA J. Numer. Anal., 24 (2004), pp. 1–19, DOI: 10.1093/imanum/24.1.1.
  43. L. Torelli and R. Vermiglio, A numerical approach for implicit non-linear neutral delay differential equations and its stability analysis, BIT, 43 (2003), pp. 195–215, DOI: 10.1023/A:1023613425081.
  44. H. Brunner and R. Vermiglio, Stability of solutions of delay functional integro-differential equations and their discretizations, Computing, 71 (2003), pp. 229–245, DOI: 10.1007/s00607-003-0022-6.
  45. D. Breda, S. Maset and R. Vermiglio, Numerical computation of characteristic roots for delay differential equations, in C. T. Abdullah, K. Gu and S.-I. Niculescu, eds., 3rd IFAC Workshop on Time Delay Systems, IFAC Proceedings Volumes 34, Elsevier, 2001, pp. 189–193, DOI: 10.1016/s1474-6670(17)32889-6.
  46. Z. Jackiewicz and R. Vermiglio, Order conditions for partitioned Runge–Kutta methods, Appl. Math., 45 (2000), pp. 301–316, DOI: 10.1023/A:1022323529349.
  47. D. Siega and R. Vermiglio, High order robust method for the integration of rapid oscillatory functions, Research report RR/UDMI/16/00, University of Udine (2000).
  48. R. Vermiglio, On the computation of the joint spectral radius: numerical experiments, Research report RR/UDMI/21/99, University of Udine (1999).
  49. Z. Jackiewicz, R. Vermiglio and M. Zennaro, Regularity properties of multistage integration methods, J. Comput. Appl. Math., 87 (1997), pp. 285–302, DOI: 10.1016/S0377-0427(97)00194-5.
  50. Z. Jackiewicz, R. Vermiglio and M. Zennaro, Regularity properties of Runge–Kutta methods for delay differential equations, Appl. Numer. Math., 24 (1997), pp. 265–278, DOI: 10.1016/S0168-9274(97)00025-1.
  51. Z. Jackiewicz, R. Vermiglio and M. Zennaro, General linear methods with external stages of different orders, BIT, 36 (1996), pp. 688–712, DOI: 10.1007/BF01733788.
  52. Z. Jackiewicz, R. Vermiglio and M. Zennaro, Regularity properties of Runge–Kutta methods for ordinary differential equations, Appl. Numer. Math., 22 (1996), pp. 251–262, DOI: 10.1016/S0168-9274(96)00036-0.
  53. A. Bellen and R. Vermiglio, Some applications of continuous Runge–Kutta methods, Appl. Numer. Math., 22 (1996), pp. 63–80, DOI: 10.1016/S0168-9274(96)00026-8.
  54. A. Bellen, V. B. Kolmanovskii, L. Torelli and R. Vermiglio, About stability of some functional differential equations of neutral type, J. Math. Anal. Appl., 189 (1995), pp. 59–84, DOI: 10.1006/jmaa.1995.1004.
  55. Z. Jackiewicz, R. Vermiglio and M. Zennaro, Variable stepsize diagonally implicit multistage integration methods for ordinary differential equations, Appl. Numer. Math., 16 (1995), pp. 343–267, DOI: 10.1016/0168-9274(94)00057-N.
  56. V. B. Kolmanovskii, L. Torelli and R. Vermiglio, Stability of some test equations with delay, SIAM J. Math. Anal., 25 (1994), pp. 948–961, DOI: 10.1137/s0036141092238023.
  57. R. Vermiglio and M. Zennaro, Multistep natural continuous extensions of Runge–Kutta methods: the potential for stable interpolation, Appl. Numer. Math., 12 (1993), pp. 521–546, DOI: 10.1016/0168-9274(93)90068-3.
  58. R. Vermiglio, Multistep high order interpolants of Runge–Kutta methods, J. Comput. Appl. Math., 45 (1993), pp. 75–88, DOI: 10.1016/0377-0427(93)90266-E.
  59. L. Torelli and R. Vermiglio, On the stability of continuous quadrature rules for differential equations with several constant delays, IMA J. Numer. Anal., 13 (1993), pp. 291–302, DOI: 10.1093/imanum/13.2.291.
  60. R. Vermiglio, On the stability of Runge–Kutta methods for delay integral equations, Numer. Math., 61 (1992), pp. 561–577, DOI: 10.1007/BF01385526.
  61. A. Bellen, Z. Jackiewicz, R. Vermiglio and M. Zennaro, Stability analysis of Runge–Kutta methods for Volterra integral equations of the second kind, IMA J. Numer. Anal., 10 (1990), pp. 103–118, DOI: 10.1093/imanum/10.1.103.
  62. A. Bellen, R. Vermiglio and M. Zennaro, Parallel ODE-solvers with stepsize control, J. Comput. Appl. Math., 31 (1990), pp. 277–293, DOI: 10.1016/0377-0427(90)90170-5.
  63. A. Bellen, Z. Jackiewicz, R. Vermiglio and M. Zennaro, A stability analysis of trapezoidal methods for Volterra integral equations with completely positive kernels, J. Math. Anal. Appl., 152 (1990), pp. 324–342, DOI: 10.1016/0022-247X(90)90068-Q.
  64. A. Bellen, Z. Jackiewicz, R. Vermiglio and M. Zennaro, Natural continuous extensions for Runge–Kutta methods for Volterra integral equations of the second kind and their applications, Math. Comp., 52 (1989), pp. 49–63, DOI: 10.1090/S0025-5718-1989-0971402-3.
  65. R. Vermiglio, Natural continuous extensions for Runge–Kutta methods for Volterra integro-differential equations, Numer. Math., 53 (1988), pp. 439–458, DOI: 10.1007/BF01396328.
  66. R. Vermiglio, A one-step subregion method for delay differential equations, Calcolo, 22 (1985), pp. 429–455, DOI: 10.1007/BF02575897.