{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:29:40Z","timestamp":1772119780857,"version":"3.50.1"},"reference-count":67,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T00:00:00Z","timestamp":1734048000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T00:00:00Z","timestamp":1734048000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["12201537"],"award-info":[{"award-number":["12201537"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1007\/s11075-024-01994-7","type":"journal-article","created":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T04:58:22Z","timestamp":1734065902000},"page":"1-31","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hamiltonian Boundary Value Methods (HBVMs) for functional differential equations with piecewise continuous arguments"],"prefix":"10.1007","volume":"101","author":[{"given":"Gianmarco","family":"Gurioli","sequence":"first","affiliation":[]},{"given":"Weijie","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Xiaoqiang","family":"Yan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,12,13]]},"reference":[{"key":"1994_CR1","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1063\/1.2216634","volume":"839","author":"U Akhmet","year":"2006","unstructured":"Akhmet, U., Oktem, H., Pickl, W., Weber, W.: An anticipatory extension of malthusian model. AIP Conf. Proc. 839, 260 (2006)","journal-title":"AIP Conf. Proc."},{"key":"1994_CR2","volume-title":"Extension of the logistic equation with piecewise constant arguments and population dynamics","author":"D Altintan","year":"2006","unstructured":"Altintan, D.: Extension of the logistic equation with piecewise constant arguments and population dynamics. Middle East Technical University, Turkey (2006)"},{"key":"1994_CR3","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/BF03028370","volume":"3","author":"CT Baker","year":"1995","unstructured":"Baker, C.T., Paul, C.A., Will\u00e9, D.R.: Issues in the numerical solution of evolutionary delay differential equations. Adv. Comput. Math. 3, 171\u2013196 (1995)","journal-title":"Adv. Comput. Math."},{"key":"1994_CR4","doi-asserted-by":"publisher","first-page":"752","DOI":"10.1145\/365844.365865","volume":"9","author":"RE Bellman","year":"1966","unstructured":"Bellman, R.E., Buell, J.D., Kalaba, R.E.: Mathematical experimentation in time-lag modulation. Commun. ACM 9, 752\u2013754 (1966)","journal-title":"Commun. ACM"},{"key":"1994_CR5","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1145\/363831.364879","volume":"8","author":"RE Bellman","year":"1965","unstructured":"Bellman, R.E., Buell, J.D., Kalaba, R.E.: Numerical integration of a differential-difference equation with a decreasing time-lag. Commun. ACM 8, 227\u2013228 (1965)","journal-title":"Commun. ACM"},{"key":"1994_CR6","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1007\/s10444-014-9390-z","volume":"41","author":"P Amodio","year":"2015","unstructured":"Amodio, P., Brugnano, L., Iavernaro, F.: Energy-conserving methods for Hamiltonian boundary value problems and applications in astrodynamics. Adv. Comput. Math. 41, 881\u2013905 (2015)","journal-title":"Adv. Comput. Math."},{"key":"1994_CR7","doi-asserted-by":"publisher","first-page":"1489","DOI":"10.1007\/s11075-019-00733-7","volume":"83","author":"P Amodio","year":"2020","unstructured":"Amodio, P., Brugnano, L., Iavernaro, F.: Analysis of Spectral Hamiltonian Boundary Value Methods (SHBVMs) for the numerical solution of ODE problems. Numer. Algorithms. 83, 1489\u20131508 (2020)","journal-title":"Numer. Algorithms."},{"key":"1994_CR8","doi-asserted-by":"publisher","first-page":"192","DOI":"10.3390\/axioms11050192","volume":"11","author":"P Amodio","year":"2022","unstructured":"Amodio, P., Brugnano, L., Iavernaro, F.: Continuous-stage Runge-Kutta approximation to differential problems. Axioms 11, 192 (2022)","journal-title":"Axioms"},{"key":"1994_CR9","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.amc.2017.04.018","volume":"318","author":"L Barletti","year":"2018","unstructured":"Barletti, L., Brugnano, L., Frasca Caccia, G., Iavernaro, F.: Energy-conserving methods for the nonlinear Schr\u00f6dinger equation. Appl. Math. Comput. 318, 3\u201318 (2018)","journal-title":"Appl. Math. Comput."},{"key":"1994_CR10","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198506546.001.0001","volume-title":"Numerical Methods for Delay Differential Equations","author":"A Bellen","year":"2003","unstructured":"Bellen, A., Zennaro, M.: Numerical Methods for Delay Differential Equations. Clarendon Press, Oxford (2003)"},{"key":"1994_CR11","doi-asserted-by":"publisher","first-page":"175","DOI":"10.3846\/1392-6292.2010.15.175-187","volume":"15","author":"H Bereketoglu","year":"2010","unstructured":"Bereketoglu, H., Seyhan, G., Ogun, A.: Advanced impulsive differential equations with piecewise constant arguments. Math. Model. Anal. 15, 175\u2013187 (2010)","journal-title":"Math. Model. Anal."},{"key":"1994_CR12","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1007\/3-540-62598-4_81","volume":"1196","author":"L Brugnano","year":"1997","unstructured":"Brugnano, L.: Boundary value method for the numerical approximation of ordinary differential equa- tions. Lect. Notes. Comput. Sc. 1196, 78\u201389 (1997)","journal-title":"Lect. Notes. Comput. Sc."},{"key":"1994_CR13","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/0096-3003(95)00308-8","volume":"81","author":"L Brugnano","year":"1997","unstructured":"Brugnano, L., Trigiante, D.: Block Boundary Value Methods for Linear Hamiltonian Systems. Appl. Math. Comput. 81, 49\u201368 (1997)","journal-title":"Appl. Math. Comput."},{"key":"1994_CR14","first-page":"233","volume":"15","author":"L Brugnano","year":"1997","unstructured":"Brugnano, L.: Essentially symplectic boundary value methods for linear Hamiltonian systems. J. Comput. Math. 15, 233\u2013252 (1997)","journal-title":"J. Comput. Math."},{"key":"1994_CR15","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/S0898-1221(98)80028-X","volume":"36","author":"L Brugnano","year":"1998","unstructured":"Brugnano, L., Trigiante, D.: Boundary value methods: the third way between linear multistep and Runge-Kutta methods. Math. Appl. Math. Comput. 36, 269\u2013284 (1998)","journal-title":"Math. Appl. Math. Comput."},{"key":"1994_CR16","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0168-9274(01)00140-4","volume":"42","author":"L Brugnano","year":"2002","unstructured":"Brugnano, L., Magherini, C.: Blended implementation of block implicit methods for ODEs. Appl. Numer. Math. 42, 29\u201345 (2002)","journal-title":"Appl. Numer. Math."},{"key":"1994_CR17","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1063\/1.3241566","volume":"1168","author":"L Brugnano","year":"2009","unstructured":"Brugnano, L., Iavernaro, F., Trigiante, D.: Hamiltonian BVMs (HBVMs): a family of \u201cdrift-free\u2019\u2019 methods for integrating polynomial Hamiltonian systems. AIP Conf. Proc. 1168, 715\u2013718 (2009)","journal-title":"AIP Conf. Proc."},{"key":"1994_CR18","doi-asserted-by":"publisher","first-page":"3890","DOI":"10.1016\/j.cam.2012.02.033","volume":"236","author":"L Brugnano","year":"2012","unstructured":"Brugnano, L., Calvo, M., Montijano, J.I.: Energy preserving methods for Poisson systems. J. Comput. Appl. Math. 236, 3890\u20133904 (2012)","journal-title":"J. Comput. Appl. Math."},{"key":"1994_CR19","doi-asserted-by":"publisher","first-page":"3905","DOI":"10.1016\/j.cam.2012.03.026","volume":"236","author":"L Brugnano","year":"2012","unstructured":"Brugnano, L., Iavernaro, F.: Line integral methods which preserve all invariants of conservative problems. J. Comput. Appl. Math. 236, 3905\u20133919 (2012)","journal-title":"J. Comput. Appl. Math."},{"key":"1994_CR20","doi-asserted-by":"publisher","first-page":"2897","DOI":"10.1137\/110856617","volume":"50","author":"L Brugnano","year":"2012","unstructured":"Brugnano, L., Iavernaro, F., Trigiante, D.: Energy and QUadratic invariants preserving integrators based upon Gauss collocation formulae. SIAM J. Numer. Anal. 50, 2897\u20132916 (2012)","journal-title":"SIAM J. Numer. Anal."},{"key":"1994_CR21","doi-asserted-by":"publisher","first-page":"611","DOI":"10.1007\/s11075-013-9769-9","volume":"65","author":"L Brugnano","year":"2014","unstructured":"Brugnano, L., Sun, Y.: Multiple invariants conserving Runge-Kutta type methods for Hamiltonian problems. Numer. Algorithms. 65, 611\u2013632 (2014)","journal-title":"Numer. Algorithms."},{"key":"1994_CR22","doi-asserted-by":"crossref","unstructured":"Brugnano, L., Iavernaro, F.: Line Integral Methods for Conservative Problems. CRC Press (2016)","DOI":"10.1201\/b19319"},{"key":"1994_CR23","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.cam.2017.11.043","volume":"335","author":"L Brugnano","year":"2018","unstructured":"Brugnano, L., Gurioli, G., Iavernaro, F.: Analysis of energy and QUadratic invariant preserving (EQUIP) methods. J. Comput. Appl. Math. 335, 51\u201373 (2018)","journal-title":"J. Comput. Appl. Math."},{"key":"1994_CR24","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1016\/j.apnum.2017.12.014","volume":"127","author":"L Brugnano","year":"2018","unstructured":"Brugnano, L., Gurioli, G., Iavernaro, F., Weinm\u00fcller, E.: Line integral solution of Hamiltonian systems with holonomic constraints. Appl. Numer. Math. 127, 56\u201377 (2018)","journal-title":"Appl. Numer. Math."},{"key":"1994_CR25","doi-asserted-by":"publisher","first-page":"1183","DOI":"10.1007\/s11075-018-0586-z","volume":"81","author":"L Brugnano","year":"2019","unstructured":"Brugnano, L., Iavernaro, F., Montijano, J.I., R\u00e1ndez, L.: Spectrally accurate space-time solution of Hamiltonian PDEs. Numer. Algorithms. 81, 1183\u20131202 (2019)","journal-title":"Numer. Algorithms."},{"key":"1994_CR26","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.cnsns.2017.12.018","volume":"60","author":"L Brugnano","year":"2018","unstructured":"Brugnano, L., Zhang, C., Li, D.: A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schr\u00f6dinger equation with wave operator. Commun. Nonlinear Sci. Numer. Simul. 60, 33\u201349 (2018)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"1994_CR27","doi-asserted-by":"publisher","first-page":"36","DOI":"10.3390\/axioms7020036","volume":"7","author":"L Brugnano","year":"2018","unstructured":"Brugnano, L., Iavernaro, F.: Line integral solution of differential problems. Axioms 7, 36 (2018)","journal-title":"Axioms"},{"key":"1994_CR28","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1007\/s11075-018-0552-9","volume":"81","author":"L Brugnano","year":"2019","unstructured":"Brugnano, L., Montijano, J.I., R\u00e1ndez, L.: On the effectiveness of spectral methods for the numerical solution of multi-frequency highly-oscillatory Hamiltonian problems. Numer. Algorithms. 81, 345\u2013376 (2019)","journal-title":"Numer. Algorithms."},{"key":"1994_CR29","doi-asserted-by":"publisher","first-page":"275","DOI":"10.3390\/math7030275","volume":"7","author":"L Brugnano","year":"2019","unstructured":"Brugnano, L., Frasca Caccia, G., Iavernaro, F.: Line integral solution of Hamiltonian PDEs. Mathematics 7, 275 (2019)","journal-title":"Mathematics"},{"key":"1994_CR30","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.cam.2018.10.014","volume":"351","author":"L Brugnano","year":"2019","unstructured":"Brugnano, L., Gurioli, G., Sun, Y.: Energy-conserving Hamiltonian Boundary Value Methods for the numerical solution of the Korteweg-de Vries equation. J. Comput. Appl. Math. 351, 117\u2013135 (2019)","journal-title":"J. Comput. Appl. Math."},{"key":"1994_CR31","doi-asserted-by":"publisher","first-page":"1343","DOI":"10.1002\/num.22353","volume":"35","author":"L Brugnano","year":"2019","unstructured":"Brugnano, L., Gurioli, G., Zhang, C.: Spectrally accurate energy-preserving methods for the numerical solution of the \u201cgood\u2019\u2019 Boussinesq equation. Numer. Math. Part. D. E. 35, 1343\u20131362 (2019)","journal-title":"Numer. Math. Part. D. E."},{"key":"1994_CR32","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1007\/s10444-022-09992-w","volume":"48","author":"L Brugnano","year":"2022","unstructured":"Brugnano, L., Frasca-Caccia, G., Iavernaro, F., Vespri, V.: A new framework for polynomial approximation to differential equations. Adv. Comput. Math. 48, 76 (2022)","journal-title":"Adv. Comput. Math."},{"key":"1994_CR33","unstructured":"Busenberg, S., Cooke, K.: Vertically transmitted diseases: models and dynamics. Springer Science & Business Media (2012)"},{"key":"1994_CR34","doi-asserted-by":"publisher","first-page":"2153","DOI":"10.1002\/mana.201800053","volume":"292","author":"S Chiu","year":"2019","unstructured":"Chiu, S., Li, T.: Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments. Math. Nachr. 292, 2153\u20132164 (2019)","journal-title":"Math. Nachr."},{"key":"1994_CR35","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/0022-247X(84)90248-8","volume":"99","author":"KL Cooke","year":"1984","unstructured":"Cooke, K.L., Wiener, J.: Retarded differential equations with piecewise constant delays. J. Math. Anal. Appl. 99, 265\u2013297 (1984)","journal-title":"J. Math. Anal. Appl."},{"key":"1994_CR36","doi-asserted-by":"publisher","first-page":"695","DOI":"10.1016\/0898-1221(86)90055-6","volume":"12","author":"KL Cooke","year":"1986","unstructured":"Cooke, K.L., Wiener, J.: Stability regions for linear equations with piecewise continuous delay. Comput. Math. Appl. 12, 695\u2013701 (1986)","journal-title":"Comput. Math. Appl."},{"key":"1994_CR37","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1017\/S0308210500026342","volume":"102","author":"JG Dos Reis","year":"1986","unstructured":"Dos Reis, J.G., Baroni, R.L.S.: On the existence of periodic solutions for autonomous retarded functional differential equations on $$R^2$$. Proc. R. Soc. Edinb. A: Math. 102, 259\u2013262 (1986)","journal-title":"Proc. R. Soc. Edinb. A: Math."},{"key":"1994_CR38","unstructured":"Driver, R.D.: Ordinary and delay differential equations. Springer Science & Business Media (2012)"},{"key":"1994_CR39","unstructured":"El\u2019sgol\u2019ts, L.E., Norkin, S.B.: Introduction to the theory and application of differential equations with deviating arguments. Academic Press (1973)"},{"key":"1994_CR40","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1016\/j.jcp.2005.05.027","volume":"211","author":"S Esedog","year":"2006","unstructured":"Esedog, S., Tsai, Y.H.R.: Threshold dynamics for the piecewise constant Mumford-Shah functional. J. Comput. Phys. 211, 367\u2013384 (2006)","journal-title":"J. Comput. Phys."},{"key":"1994_CR41","first-page":"573","volume":"8","author":"M Esmaeilzadeh","year":"2020","unstructured":"Esmaeilzadeh, M., Najafi, H., Aminikhah, H.: A numerical scheme for diffusion-convection equation with piecewise constant arguments. Comput. Methods. Differ. 8, 573\u2013584 (2020)","journal-title":"Comput. Methods. Differ."},{"key":"1994_CR42","doi-asserted-by":"crossref","unstructured":"Feng, Z., Wang, Y., Ma, X.: Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments. Adv. Differ. Equ. 1\u201322 (2020)","DOI":"10.1186\/s13662-020-02699-6"},{"key":"1994_CR43","doi-asserted-by":"crossref","unstructured":"Gopalsamy, K.: Stability and oscillations in delay differential equations of population dynamics. Springer Science & Business Media (1992)","DOI":"10.1007\/978-94-015-7920-9"},{"key":"1994_CR44","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1006\/jmaa.1998.5984","volume":"224","author":"K Gopalsamy","year":"1998","unstructured":"Gopalsamy, K., Liu, P.: Persistence and global stability in a population model. J. Math. Anal. Appl. 224, 59\u201380 (1998)","journal-title":"J. Math. Anal. Appl."},{"key":"1994_CR45","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/0022-247X(74)90162-0","volume":"48","author":"JL Kaplan","year":"1974","unstructured":"Kaplan, J.L., Yorke, J.A.: Ordinary differential equations which yield periodic solutions of differential delay equations. J. Math. Anal. Appl. 48, 317\u2013324 (1974)","journal-title":"J. Math. Anal. Appl."},{"key":"1994_CR46","unstructured":"Kolmanovskii, V., Myshkis, A.: Applied theory of functional differential equations. Springer Science & Business Media (2012)"},{"key":"1994_CR47","first-page":"1","volume":"241","author":"P Kumar","year":"2013","unstructured":"Kumar, P., Pandey, N.D., Bahuguna, D.: Existence of piecewise continuous mild solutions for impulsive functional differential equations with iterated deviating arguments. Electron. J. Differ. Eq. 241, 1\u201315 (2013)","journal-title":"Electron. J. Differ. Eq."},{"key":"1994_CR48","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1016\/j.amc.2013.12.013","volume":"228","author":"H Liang","year":"2014","unstructured":"Liang, H., Liu, M., Yang, Z.: Stability analysis of Runge-Kutta methods for systems $$u^{\\prime }\\left( t \\right) = Lu\\left( t \\right) + Mu\\left( {\\lfloor t \\rfloor } \\right)$$. Appl. Math. Comput. 228, 463\u2013476 (2014)","journal-title":"Appl. Math. Comput."},{"key":"1994_CR49","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1016\/j.cam.2003.04.002","volume":"166","author":"M Liu","year":"2004","unstructured":"Liu, M., Song, M., Yang, Z.: Stability of Rung-Kutta methods in the numerical solution of equation $$u^{\\prime }\\left( t \\right) = au\\left( t \\right) + {a_0}u\\left( {\\lfloor t \\rfloor } \\right)$$. J. Comput. Appl. Math. 166, 361\u2013370 (2004)","journal-title":"J. Comput. Appl. Math."},{"key":"1994_CR50","doi-asserted-by":"publisher","first-page":"1113","DOI":"10.1016\/j.camwa.2009.07.030","volume":"58","author":"M Liu","year":"2009","unstructured":"Liu, M., Gao, J., Yang, Z.: Preservation of oscillations of the Runge-Kutta method for equation $$x^{\\prime }\\left( t \\right) + ax\\left( t \\right) + {a_1}x\\left( \\lfloor {t - 1}\\rfloor \\right) = 0$$. Comput. Math. Appl. 58, 1113\u20131125 (2009)","journal-title":"Comput. Math. Appl."},{"key":"1994_CR51","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/j.cam.2014.11.059","volume":"280","author":"X Liu","year":"2015","unstructured":"Liu, X., Liu, M.: Asymptotic stability of Runge-Kutta methods for nonlinear differential equations with piecewise continuous arguments. J. Comput. Appl. Math. 280, 265\u2013274 (2015)","journal-title":"J. Comput. Appl. Math."},{"key":"1994_CR52","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1016\/j.apnum.2017.01.012","volume":"115","author":"C Li","year":"2017","unstructured":"Li, C., Zhang, C.: Block boundary value methods applied to functional differential equations with piece- wise continuous argument. Appl. Numer. Math. 115, 214\u2013224 (2017)","journal-title":"Appl. Numer. Math."},{"key":"1994_CR53","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1016\/j.apnum.2019.10.005","volume":"150","author":"C Zhang","year":"2019","unstructured":"Zhang, C., Li, C., Jiang, Y.: Extended block boundary value methods for neutral equations with piece- wise constant argument. Appl. Numer. Math. 150, 182\u2013193 (2019)","journal-title":"Appl. Numer. Math."},{"key":"1994_CR54","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/j.amc.2011.05.042","volume":"218","author":"W Lv","year":"2011","unstructured":"Lv, W., Yang, Z., Liu, M.: Numerical stability analysis of differential equations with piecewise constant arguments with complex coefficients. Appl. Math. Comput. 218, 45\u201354 (2011)","journal-title":"Appl. Math. Comput."},{"key":"1994_CR55","doi-asserted-by":"publisher","first-page":"4085","DOI":"10.1016\/j.jde.2010.10.023","volume":"250","author":"J Mallet-Paret","year":"2011","unstructured":"Mallet-Paret, J., Nussbaum, R.D.: Stability of periodic solutions of state-dependent delay-differential equations. J Diff. Equ. 250, 4085\u20134103 (2011)","journal-title":"J Diff. Equ."},{"key":"1994_CR56","first-page":"173","volume":"32","author":"AD Myshkis","year":"1977","unstructured":"Myshkis, A.D.: On certain problems in the theory of differential equations with deviating arguments. Uspekhi Mat. Nuuk 32, 173\u2013202 (1977)","journal-title":"Uspekhi Mat. Nuuk"},{"key":"1994_CR57","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1090\/S0002-9904-1973-13330-0","volume":"79","author":"RD Nussbaum","year":"1973","unstructured":"Nussbaum, R.D.: Periodic solutions of some nonlinear, autonomous functional differential equations. Bull. Amer. Math. Soc. 79, 811\u2013814 (1973)","journal-title":"Bull. Amer. Math. Soc."},{"key":"1994_CR58","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/0022-0396(79)90016-0","volume":"34","author":"RD Nussbaum","year":"1979","unstructured":"Nussbaum, R.D.: Uniqueness and nonuniqueness for periodic solutions of $$x^{\\prime }(t)=-g(x(t-1))$$. J Diff. Equ. 34, 25\u201354 (1979)","journal-title":"J Diff. Equ."},{"key":"1994_CR59","unstructured":"Rodney, D.: A functional-differential system of neutral type arising in a two-body problem of classical electrodynamics. Academic Press (1963)"},{"key":"1994_CR60","unstructured":"Sobolev, L.: Partial differential equations of mathematical physics. Courier Corporation (1964)"},{"key":"1994_CR61","doi-asserted-by":"publisher","first-page":"4002","DOI":"10.1016\/j.amc.2010.10.006","volume":"217","author":"M Song","year":"2010","unstructured":"Song, M., Liu, X.: The improved linear multistep methods for differential equations with piecewise continuous arguments. Appl. Math. Comput. 217, 4002\u20134009 (2010)","journal-title":"Appl. Math. Comput."},{"key":"1994_CR62","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/BF01273745","volume":"1","author":"H-O Walther","year":"1975","unstructured":"Walther, H.-O.: Existence of a non-constant periodic solution of a nonlinear autonomous functional differential equation representing the growth of a single species population. J. Math. Biol. 1, 227\u2013240 (1975)","journal-title":"J. Math. Biol."},{"key":"1994_CR63","doi-asserted-by":"publisher","first-page":"983","DOI":"10.1016\/j.aml.2007.10.014","volume":"21","author":"W Wang","year":"2008","unstructured":"Wang, W., Li, S.: Dissipativity of Runge-Kutta methods for neutral delay differential equations with piecewise constant delay. Appl. Math. Lett. 21, 983\u2013991 (2008)","journal-title":"Appl. Math. Lett."},{"key":"1994_CR64","doi-asserted-by":"publisher","first-page":"4590","DOI":"10.1016\/j.amc.2012.10.070","volume":"219","author":"W Wang","year":"2013","unstructured":"Wang, W.: Stability of solutions of nonlinear neutral differential equations with piecewise constant delay and their discretizations. Appl. Math. Comput. 219, 4590\u20134600 (2013)","journal-title":"Appl. Math. Comput."},{"key":"1994_CR65","first-page":"393","volume":"23","author":"L Wen","year":"2005","unstructured":"Wen, L., Li, S.: Stability of theoretical solution and numerical solution of nonlinear differential equations with piecewise delays. J. Comput. Math. 23, 393\u2013400 (2005)","journal-title":"J. Comput. Math."},{"key":"1994_CR66","doi-asserted-by":"publisher","DOI":"10.1142\/1860","volume-title":"Generalized Solutions of Differential Equations","author":"J Wiener","year":"1993","unstructured":"Wiener, J.: Generalized Solutions of Differential Equations. World Scientific, Singapore (1993)"},{"key":"1994_CR67","doi-asserted-by":"publisher","first-page":"921","DOI":"10.1007\/s11075-020-00993-8","volume":"87","author":"C Zhang","year":"2021","unstructured":"Zhang, C., Yan, X.: Convergence and stability of extended BBVMs for nonlinear delay-differential-algebraic equations with piecewise continuous arguments. Numer. Algorithms. 87, 921\u2013937 (2021)","journal-title":"Numer. Algorithms."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01994-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-024-01994-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01994-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T08:02:28Z","timestamp":1767772948000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-024-01994-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,13]]},"references-count":67,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["1994"],"URL":"https:\/\/doi.org\/10.1007\/s11075-024-01994-7","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-4085234\/v1","asserted-by":"object"}]},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,13]]},"assertion":[{"value":"12 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 December 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 December 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}