Amodio, Pierluigi; Brugnano, Luigi; Iavernaro, Felice (Spectral) Chebyshev collocation methods for solving differential equations. (English) Zbl 1523.65100 Numer. Algorithms 93, No. 4, 1613-1638 (2023). MSC: 65P10 65L60 65L06 65L05 PDFBibTeX XMLCite \textit{P. Amodio} et al., Numer. Algorithms 93, No. 4, 1613--1638 (2023; Zbl 1523.65100) Full Text: DOI arXiv
Brugnano, Luigi; Frasca-Caccia, Gianluca; Iavernaro, Felice; Vespri, Vincenzo A new framework for polynomial approximation to differential equations. (English) Zbl 1507.65115 Adv. Comput. Math. 48, No. 6, Paper No. 76, 36 p. (2022). MSC: 65L05 65L03 65L06 65P10 PDFBibTeX XMLCite \textit{L. Brugnano} et al., Adv. Comput. Math. 48, No. 6, Paper No. 76, 36 p. (2022; Zbl 1507.65115) Full Text: DOI arXiv
Brugnano, Luigi; Iavernaro, Felice A general framework for solving differential equations. (English) Zbl 1503.65312 Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 68, No. 2, 243-258 (2022). MSC: 65P10 65L05 65L06 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{F. Iavernaro}, Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 68, No. 2, 243--258 (2022; Zbl 1503.65312) Full Text: DOI
Amodio, Pierluigi; Brugnano, Luigi; Iavernaro, Felice Arbitrary high-order methods for one-sided direct event location in discontinuous differential problems with nonlinear event function. (English) Zbl 1491.65062 Appl. Numer. Math. 179, 39-49 (2022). MSC: 65L05 65L06 34A36 PDFBibTeX XMLCite \textit{P. Amodio} et al., Appl. Numer. Math. 179, 39--49 (2022; Zbl 1491.65062) Full Text: DOI arXiv
Amodio, Pierluigi; Brugnano, Luigi; Iavernaro, Felice Continuous-Stage Runge-Kutta approximation to Differential Problems. arXiv:2203.11189 Preprint, arXiv:2203.11189 [math.NA] (2022). MSC: 65L06 65P10 65L05 BibTeX Cite \textit{P. Amodio} et al., ``Continuous-Stage Runge-Kutta approximation to Differential Problems'', Preprint, arXiv:2203.11189 [math.NA] (2022) Full Text: DOI arXiv OA License
Amodio, P.; Brugnano, L.; Frasca-Caccia, G.; Iavernaro, F. Arbitrarily high-order energy-conserving methods for Hamiltonian problems with quadratic holonomic constraints. arXiv:2203.03275 Preprint, arXiv:2203.03275 [math.NA] (2022). MSC: 65P10 65L80 65L06 BibTeX Cite \textit{P. Amodio} et al., ``Arbitrarily high-order energy-conserving methods for Hamiltonian problems with quadratic holonomic constraints'', Preprint, arXiv:2203.03275 [math.NA] (2022) Full Text: DOI arXiv OA License
Brugnano, Luigi; Gurioli, Gianmarco; Zhang, Chengjian Spectrally accurate energy-preserving methods for the numerical solution of the “good” Boussinesq equation. (English) Zbl 1418.65117 Numer. Methods Partial Differ. Equations 35, No. 4, 1343-1362 (2019). MSC: 65M20 65L06 65P10 35Q35 76B15 PDFBibTeX XMLCite \textit{L. Brugnano} et al., Numer. Methods Partial Differ. Equations 35, No. 4, 1343--1362 (2019; Zbl 1418.65117) Full Text: DOI arXiv
Brugnano, Luigi; Gurioli, Gianmarco; Sun, Yajuan Energy-conserving Hamiltonian boundary value methods for the numerical solution of the Korteweg-de Vries equation. (English) Zbl 1414.65024 J. Comput. Appl. Math. 351, 117-135 (2019). Reviewer: Anouar Ben Mabrouk (Sousse) MSC: 65M70 65M60 35Q35 35C08 37K40 65L06 65L12 PDFBibTeX XMLCite \textit{L. Brugnano} et al., J. Comput. Appl. Math. 351, 117--135 (2019; Zbl 1414.65024) Full Text: DOI
Brugnano, Luigi; Frasca-Caccia, Gianluca; Iavernaro, Felice Line Integral solution of Hamiltonian PDEs. arXiv:1903.06704 Preprint, arXiv:1903.06704 [math.NA] (2019). MSC: 65P10 65M70 65M20 65L05 65L06 BibTeX Cite \textit{L. Brugnano} et al., ``Line Integral solution of Hamiltonian PDEs'', Preprint, arXiv:1903.06704 [math.NA] (2019) Full Text: DOI arXiv OA License
Brugnano, Luigi; Iavernaro, Felice Line integral solution of differential problems. (English) Zbl 1432.65181 Axioms 7, No. 2, Paper No. 36, 28 p. (2018). MSC: 65P10 65L06 65L05 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{F. Iavernaro}, Axioms 7, No. 2, Paper No. 36, 28 p. (2018; Zbl 1432.65181) Full Text: DOI
Brugnano, Luigi; Gurioli, Gianmarco; Iavernaro, Felice Analysis of energy and quadratic invariant preserving (EQUIP) methods. (English) Zbl 1444.65069 J. Comput. Appl. Math. 335, 51-73 (2018). MSC: 65P10 65L05 65L06 PDFBibTeX XMLCite \textit{L. Brugnano} et al., J. Comput. Appl. Math. 335, 51--73 (2018; Zbl 1444.65069) Full Text: DOI arXiv
Brugnano, Luigi; Iavernaro, Felice Line integral methods for conservative problems. (English) Zbl 1335.65097 Monographs and Research Notes in Mathematics. Boca Raton, FL: CRC Press (ISBN 978-1-4822-6384-8/hbk; 978-1-4822-6385-5/ebook). xvi, 222 p. (2016). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65P10 65-02 65L06 37M15 37K05 37J05 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{F. Iavernaro}, Line integral methods for conservative problems. Boca Raton, FL: CRC Press (2016; Zbl 1335.65097) Full Text: DOI
Brugnano, Luigi; Iavernaro, Felice; Trigiante, Donato Reprint of “Analysis of Hamiltonian boundary value methods (HBVMs): a class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems”. (English) Zbl 1329.65304 Commun. Nonlinear Sci. Numer. Simul. 21, No. 1-3, 34-51 (2015). MSC: 65P10 65L06 PDFBibTeX XMLCite \textit{L. Brugnano} et al., Commun. Nonlinear Sci. Numer. Simul. 21, No. 1--3, 34--51 (2015; Zbl 1329.65304) Full Text: DOI
Amodio, Pierluigi; Brugnano, Luigi; Iavernaro, Felice Energy-conserving methods for Hamiltonian boundary value problems and applications in astrodynamics. (English) Zbl 1327.65267 Adv. Comput. Math. 41, No. 4, 881-905 (2015). MSC: 65P10 65L10 65L06 PDFBibTeX XMLCite \textit{P. Amodio} et al., Adv. Comput. Math. 41, No. 4, 881--905 (2015; Zbl 1327.65267) Full Text: DOI arXiv
Brugnano, Luigi; Iavernaro, Felice; Trigiante, Donato Analysis of Hamiltonian boundary value methods (HBVMs): A class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems. (English) Zbl 1304.65262 Commun. Nonlinear Sci. Numer. Simul. 20, No. 3, 650-667 (2015); reprint ibid. 21, No. 1-3, 34-51 (2015). MSC: 65P10 65L06 PDFBibTeX XMLCite \textit{L. Brugnano} et al., Commun. Nonlinear Sci. Numer. Simul. 20, No. 3, 650--667 (2015; Zbl 1304.65262) Full Text: DOI arXiv
Brugnano, Luigi; Iavernaro, Felice; Magherini, Cecilia Efficient implementation of Radau collocation methods. (English) Zbl 1302.65160 Appl. Numer. Math. 87, 100-113 (2015). MSC: 65L04 65L05 65L06 65L60 65L20 34A34 PDFBibTeX XMLCite \textit{L. Brugnano} et al., Appl. Numer. Math. 87, 100--113 (2015; Zbl 1302.65160) Full Text: DOI arXiv Link
Brugnano, Luigi; Frasca Caccia, Gianluca; Iavernaro, Felice Hamiltonian boundary value methods (HBVMs) and their efficient implementation. (English) Zbl 1310.65159 Math. Eng. Sci. Aerosp. MESA 5, No. 4, 343-411 (2014). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65P10 65L06 65L20 65L10 37J05 37M15 PDFBibTeX XMLCite \textit{L. Brugnano} et al., Math. Eng. Sci. Aerosp. MESA 5, No. 4, 343--411 (2014; Zbl 1310.65159) Full Text: Link
Brugnano, Luigi; Frasca Caccia, Gianluca; Iavernaro, Felice Efficient implementation of Gauss collocation and Hamiltonian boundary value methods. (English) Zbl 1291.65357 Numer. Algorithms 65, No. 3, 633-650 (2014). MSC: 65P10 37M15 65L06 65L60 34A34 65L20 PDFBibTeX XMLCite \textit{L. Brugnano} et al., Numer. Algorithms 65, No. 3, 633--650 (2014; Zbl 1291.65357) Full Text: DOI arXiv
Brugnano, Luigi; Sun, Yajuan Multiple invariants conserving Runge-Kutta type methods for Hamiltonian problems. (English) Zbl 1291.65358 Numer. Algorithms 65, No. 3, 611-632 (2014). MSC: 65P10 37M15 65L06 65L05 34A34 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{Y. Sun}, Numer. Algorithms 65, No. 3, 611--632 (2014; Zbl 1291.65358) Full Text: DOI arXiv
Brugnano, Luigi; Iavernaro, Felice; Trigiante, Donato A two-step, fourth-order method with energy preserving properties. (English) Zbl 1305.65238 Comput. Phys. Commun. 183, No. 9, 1860-1868 (2012). MSC: 65P10 37M15 65L06 PDFBibTeX XMLCite \textit{L. Brugnano} et al., Comput. Phys. Commun. 183, No. 9, 1860--1868 (2012; Zbl 1305.65238) Full Text: DOI arXiv
Brugnano, Luigi; Iavernaro, Felice; Trigiante, Donato Energy- and quadratic invariants-preserving integrators based upon Gauss collocation formulae. (English) Zbl 1261.65130 SIAM J. Numer. Anal. 50, No. 6, 2897-2916 (2012). MSC: 65P10 65L05 37M15 65L06 PDFBibTeX XMLCite \textit{L. Brugnano} et al., SIAM J. Numer. Anal. 50, No. 6, 2897--2916 (2012; Zbl 1261.65130) Full Text: DOI arXiv
Brugnano, L.; Calvo, M.; Montijano, J. I.; Rández, L. Energy-preserving methods for Poisson systems. (English) Zbl 1247.65092 J. Comput. Appl. Math. 236, No. 16, 3890-3904 (2012). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65L05 65P10 34A30 65L06 37M15 PDFBibTeX XMLCite \textit{L. Brugnano} et al., J. Comput. Appl. Math. 236, No. 16, 3890--3904 (2012; Zbl 1247.65092) Full Text: DOI
Brugnano, Luigi; Iavernaro, Felice; Trigiante, Donato Isospectral Property of Hamiltonian Boundary Value Methods (HBVMs) and their connections with Runge-Kutta collocation methods. arXiv:1002.4394 Preprint, arXiv:1002.4394 [math.NA] (2010). MSC: 65P10 65L05 65L06 65L80 65H10 BibTeX Cite \textit{L. Brugnano} et al., ``Isospectral Property of Hamiltonian Boundary Value Methods (HBVMs) and their connections with Runge-Kutta collocation methods'', Preprint, arXiv:1002.4394 [math.NA] (2010) Full Text: arXiv OA License
Brugnano, Luigi; Iavernaro, Felice; Trigiante, Donato Isospectral Property of Hamiltonian Boundary Value Methods (HBVMs) and their blended implementation. arXiv:1002.1387 Preprint, arXiv:1002.1387 [math.NA] (2010). MSC: 65P10 65L05 65L06 65L80 65H10 BibTeX Cite \textit{L. Brugnano} et al., ``Isospectral Property of Hamiltonian Boundary Value Methods (HBVMs) and their blended implementation'', Preprint, arXiv:1002.1387 [math.NA] (2010) Full Text: arXiv OA License
Brugnano, Luigi; Magherini, Cecilia Recent advances in linear analysis of convergence for splittings for solving ODE problems. (English) Zbl 1162.65039 Appl. Numer. Math. 59, No. 3-4, 542-557 (2009). Reviewer: Othmar Koch (Baden) MSC: 65L05 65L06 65H10 34A34 65L20 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{C. Magherini}, Appl. Numer. Math. 59, No. 3--4, 542--557 (2009; Zbl 1162.65039) Full Text: DOI
Brugnano, Luigi; Magherini, Cecilia Blended general linear methods based on generalized BDF. (English) Zbl 1167.65397 Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics 2008, Psalidi, Kos, Greece, 16–20 September 2008. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0576-9/hbk). AIP Conference Proceedings 1048, 871-874 (2008). MSC: 65L06 65L05 34A34 65L20 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{C. Magherini}, AIP Conf. Proc. 1048, 871--874 (2008; Zbl 1167.65397)
Brugnano, Luigi; Magherini, Cecilia Economical error estimates for block implicit methods for ODEs via deferred correction. (English) Zbl 1095.65080 Appl. Numer. Math. 56, No. 5, 608-617 (2006). Reviewer: Ivan Secrieru (Chişinău) MSC: 65L70 65L05 65L06 34A34 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{C. Magherini}, Appl. Numer. Math. 56, No. 5, 608--617 (2006; Zbl 1095.65080) Full Text: DOI
Brugnano, Luigi; Magherini, Cecilia; Mugnai, Filippo Blended implicit methods for the numerical solution of DAE problems. (English) Zbl 1088.65076 J. Comput. Appl. Math. 189, No. 1-2, 34-50 (2006). Reviewer: Emil Minchev (Russe) MSC: 65L80 65L05 65L06 65H10 34A09 PDFBibTeX XMLCite \textit{L. Brugnano} et al., J. Comput. Appl. Math. 189, No. 1--2, 34--50 (2006; Zbl 1088.65076) Full Text: DOI
Brugnano, Luigi; Magherini, Cecilia Some linear algebra issues concerning the implementation of blended implicit methods. (English) Zbl 1164.65438 Numer. Linear Algebra Appl. 12, No. 2-3, 305-314 (2005). Reviewer: Jan Chleboun (Praha) MSC: 65L05 65L06 65L20 65F10 65Y15 34A34 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{C. Magherini}, Numer. Linear Algebra Appl. 12, No. 2--3, 305--314 (2005; Zbl 1164.65438) Full Text: DOI
Carreras, Giulia; Brugnano, Luigi; Burrage, Kevin On the convergence of LMF-type methods for SODEs. (English) Zbl 1167.65321 Mediterr. J. Math. 1, No. 3, 297-313 (2004). MSC: 65C30 60H10 65L05 65L06 PDFBibTeX XMLCite \textit{G. Carreras} et al., Mediterr. J. Math. 1, No. 3, 297--313 (2004; Zbl 1167.65321) Full Text: DOI
Brugnano, Luigi; Magherini, Cecilia The BiM code for the numerical solution of ODEs. (English) Zbl 1038.65063 J. Comput. Appl. Math. 164-165, 145-158 (2004). MSC: 65L06 65L05 65L20 65H10 34A34 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{C. Magherini}, J. Comput. Appl. Math. 164--165, 145--158 (2004; Zbl 1038.65063) Full Text: DOI
Brugnano, Luigi; Magherini, Cecilia Blended implementation of block implicit methods for ODEs. (English) Zbl 1006.65078 Appl. Numer. Math. 42, No. 1-3, 29-45 (2002). Reviewer: Ivan Secrieru (Chişinău) MSC: 65L06 65L05 65Y05 34A34 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{C. Magherini}, Appl. Numer. Math. 42, No. 1--3, 29--45 (2002; Zbl 1006.65078) Full Text: DOI
Brugnano, Luigi; Trigiante, Donato Block implicit methods for ODEs. (English) Zbl 1019.65051 Trigiante, Donato (ed.), Recent trends in numerical analysis. Dedicated to the 65th birthday of Professor I. Galligani. Huntington, NY: Nova Science Publishers. Adv. Theory Comput. Comput. Math. 3, 81-105 (2001). MSC: 65L06 65L05 65Y05 65L20 34A34 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{D. Trigiante}, Adv. Theory Comput. Comput. Math. 3, 81--105 (2001; Zbl 1019.65051)
Brugnano, Luigi Blended block BVMs (B\(_3\)VMs): A family of economical implicit methods for ODEs. (English) Zbl 0982.65084 J. Comput. Appl. Math. 116, No. 1, 41-62 (2000). Reviewer: Manuel Calvo (Zaragoza) MSC: 65L06 65L20 34A34 65L05 PDFBibTeX XMLCite \textit{L. Brugnano}, J. Comput. Appl. Math. 116, No. 1, 41--62 (2000; Zbl 0982.65084) Full Text: DOI
Brugnano, Luigi; Trigiante, Donato Boundary value methods: The third way between linear multistep and Runge-Kutta methods. (English) Zbl 0933.65082 Comput. Math. Appl. 36, No. 10-12, 269-284 (1998). MSC: 65L06 65L05 34A34 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{D. Trigiante}, Comput. Math. Appl. 36, No. 10--12, 269--284 (1998; Zbl 0933.65082) Full Text: DOI
Brugnano, Luigi; Trigiante, Donato Solving differential equations by multistep. Initial and boundary value methods. (English) Zbl 0934.65074 Stability and Control: Theory, Methods and Applications. 6. London: Gordon and Breach. 448 p. (1998). Reviewer: R.D.Grigorieff (Berlin) MSC: 65L06 65-02 65L10 65L20 65L05 34A34 34B15 65P10 37M15 65M20 65Y05 65L80 65L50 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{D. Trigiante}, Solving differential equations by multistep. Initial and boundary value methods. London: Gordon and Breach (1998; Zbl 0934.65074)
Amodio, Pierluigi; Brugnano, Luigi A note on the efficient implementation of implicit methods for ODEs. (English) Zbl 0897.65052 J. Comput. Appl. Math. 87, No. 1, 1-9 (1997). Reviewer: H.Ade (Mainz) MSC: 65L06 65L05 65Y20 34A34 PDFBibTeX XMLCite \textit{P. Amodio} and \textit{L. Brugnano}, J. Comput. Appl. Math. 87, No. 1, 1--9 (1997; Zbl 0897.65052) Full Text: DOI
Amodio, Pierluigi; Brugnano, Luigi Parallel ODE solvers based on block BVMs. (English) Zbl 0884.65074 Adv. Comput. Math. 7, No. 1-2, 5-26 (1997). Reviewer: I.Coroian (Baia Mare) MSC: 65L05 65L06 65L20 34A34 PDFBibTeX XMLCite \textit{P. Amodio} and \textit{L. Brugnano}, Adv. Comput. Math. 7, No. 1--2, 5--26 (1997; Zbl 0884.65074) Full Text: DOI
Brugnano, L. Essentially symplectic boundary value methods for linear Hamiltonian systems. (English) Zbl 0884.65070 J. Comput. Math. 15, No. 3, 233-252 (1997). Reviewer: S.Yanchuk (Kiev) MSC: 65L05 37J99 70H05 65L12 65L06 PDFBibTeX XMLCite \textit{L. Brugnano}, J. Comput. Math. 15, No. 3, 233--252 (1997; Zbl 0884.65070)
Brugnano, Luigi; Trigiante, Donato Block boundary value methods for linear Hamiltonian systems. (English) Zbl 0889.65076 Appl. Math. Comput. 81, No. 1, 49-68 (1997). Reviewer: Werner M.Seiler (Mannheim) MSC: 65L05 37J99 65L06 70H05 65L20 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{D. Trigiante}, Appl. Math. Comput. 81, No. 1, 49--68 (1997; Zbl 0889.65076) Full Text: DOI
Brugnano, Luigi; Trigiante, Donato Convergence and stability of boundary value methods for ordinary differential equations. (English) Zbl 0855.65087 J. Comput. Appl. Math. 66, No. 1-2, 97-109 (1996). Reviewer: M.Bartušek (Brno) MSC: 65L06 65L20 65L05 34A34 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{D. Trigiante}, J. Comput. Appl. Math. 66, No. 1--2, 97--109 (1996; Zbl 0855.65087) Full Text: DOI
Brugnano, Luigi; Trigiante, Donato High-order multistep methods for boundary value problems. (English) Zbl 0837.65081 Appl. Numer. Math. 18, No. 1-3, 79-94 (1995). Reviewer: E.Hairer (Genève) MSC: 65L06 65L10 34B05 PDFBibTeX XMLCite \textit{L. Brugnano} and \textit{D. Trigiante}, Appl. Numer. Math. 18, No. 1--3, 79--94 (1995; Zbl 0837.65081) Full Text: DOI