This work is licensed under the Creative Commons Attribution 4.0 Public License.
Alamo, A., Sanz-Serna, J.M., (2016), A technique for studying strong and weak local errors of splitting stochastic integrators. SIAM J. Numer. Anal. 54, 3239–3257.AlamoA.Sanz-SernaJ.M.2016A technique for studying strong and weak local errors of splitting stochastic integrators5432393257Search in Google Scholar
Alamo, A., Sanz-Serna, J.M., (2019), Word combinatorics for stochastic differential equations: splitting integrators, Comm. on Pure Applied Anal. 18, 2163-2195.AlamoA.Sanz-SernaJ.M.2019Word combinatorics for stochastic differential equations: splitting integrators1821632195Search in Google Scholar
Calvo, M.P., Chartier, Ph., Murua A., and Sanz-Serna, J.M., (2011a), Numerical stroboscopic averaging for ODEs and DAEs. Appl. Numer. Math. 61, 1077–1095.CalvoM.P.ChartierPh.MuruaA.Sanz-SernaJ.M.2011aNumerical stroboscopic averaging for ODEs and DAEs6110771095Search in Google Scholar
Calvo, M.P., Chartier, Ph., Murua, A., and Sanz-Serna, J.M., (2011b) A stroboscopic method for highly oscillatory problems. In: B. Engquist, O. Runborg and R. Tsai (eds.) Numerical Analysis and Multiscale Computations, pp. 73–87. Springer, New York.CalvoM.P.ChartierPh.MuruaA.Sanz-SernaJ.M.2011bA stroboscopic method for highly oscillatory problemsEngquistB.RunborgO.TsaiR.7387SpringerNew YorkSearch in Google Scholar
Calvo, M.P., Zhu, B., and Sanz-Serna J.M., (2019), High-order stroboscopic averaging methods for highly oscillatory delay problems, submitted.CalvoM.P.ZhuB.Sanz-SernaJ.M.2019High-order stroboscopic averaging methods for highly oscillatory delay problemsSearch in Google Scholar
Chartier, Ph., Murua, A., and Sanz-Serna, J.M., (2010), Higher-order averaging, formal series and numerical integration I: B-series, Found. Comput. Math. 10, 695-727.ChartierPh.MuruaA.Sanz-SernaJ.M.2010Higher-order averaging, formal series and numerical integration I: B-series10695727Search in Google Scholar
Chartier, Ph., Murua, A., and Sanz-Serna, J.M., (2012a), Higher-order averaging, formal series and numerical integration II: the quasi-periodic case. Found. Comput. Maths. 12, 471-508.ChartierPh.MuruaA.Sanz-SernaJ.M.2012aHigher-order averaging, formal series and numerical integration II: the quasi-periodic case12471508Search in Google Scholar
Chartier, Ph., Murua, A., and Sanz-Serna, J.M., (2012b), A formal series approach to averaging: exponentially small error estimates. DCDS A 32, 3009-3027.ChartierPh.MuruaA.Sanz-SernaJ.M.2012bA formal series approach to averaging: exponentially small error estimates3230093027Search in Google Scholar
Chartier, Ph., Murua, A., and Sanz-Serna, J.M., (2015), Higher-order averaging, formal series and numerical integration III: error bounds, Found. Comput. Maths. 15, 591-612.ChartierPh.MuruaA.Sanz-SernaJ.M.2015Higher-order averaging, formal series and numerical integration III: error bounds15591612Search in Google Scholar
Chartier, Ph., Murua, A., and Sanz-Serna, J.M., (2017), Erratum to: Higher-order averaging, formal series and numerical integration II: the quasi-periodic case, Found. Comput. Maths. 17, 625-626.ChartierPh.MuruaA.Sanz-SernaJ.M.2017Erratum to: Higher-order averaging, formal series and numerical integration II: the quasi-periodic case17625626Search in Google Scholar
Daza, A., Wagemakers, A., Rajasekar, S., and Sanjuán, M.A.F., (2013), Vibrational resonance in a time-delayed genetic toggle switch. Commun. Nonlinear Sci. Numer. Simul. 18, 411–416.DazaA.WagemakersA.RajasekarS.SanjuánM.A.F.2013Vibrational resonance in a time-delayed genetic toggle switch18411416Search in Google Scholar
Gardner, T.S., Cantor, C.R., and Collins, J.J., (2000), Construction of a genetic toggle switch in Escherichia coli. Nature 403, 393–342.GardnerT.S.CantorC.R.CollinsJ.J.2000Construction of a genetic toggle switch in Escherichia coli403393342Search in Google Scholar
Landa, P.S., McClintock, P.V.E., (2000), Vibrational resonance. J. Phys. A 33, L433.LandaP.S.McClintockP.V.E.2000Vibrational resonance33L433Search in Google Scholar
Lehman, B., Weibel, S.P., (1999), Fundamental theorems of averaging for functional differential equations. J. Diff. Eqns. 152, 160–190.LehmanB.WeibelS.P.1999Fundamental theorems of averaging for functional differential equations152160190Search in Google Scholar
Murua, A., Sanz-Serna, J.M., (2016a), Vibrational resonance: a study with high-order word-series averaging. Applied Mathematics and Nonlinear Sciences 1, 239-246.MuruaA.Sanz-SernaJ.M.2016aVibrational resonance: a study with high-order word-series averaging1239246Search in Google Scholar
Murua, A., Sanz-Serna, J.M., (2016b), Word series for dynamical systems and their numerical integrators. Found. Comput. Maths. 17, 675-712.MuruaA.Sanz-SernaJ.M.2016bWord series for dynamical systems and their numerical integrators17675712Search in Google Scholar
Murua, A., Sanz-Serna, J.M., (2016c), Computing normal forms and formal invariants of dynamical systems by means of word series. Nonlinear Analysis 138, 326-345.MuruaA.Sanz-SernaJ.M.2016cComputing normal forms and formal invariants of dynamical systems by means of word series138326345Search in Google Scholar
Murua, A., Sanz-Serna, J.M., (2018a), Averaging and computing normal forms with word series algorithms. In: K. Ebrahimi Fard and M. Barbero Liñán (eds.) Discrete Mechanics, Geometric Integration and Lie-Butcher Series (DMGILBS, Madrid, May 2015), pp. 115-137. Springer, Berlin.MuruaA.Sanz-SernaJ.M.2018aAveraging and computing normal forms with word series algorithmsEbrahimi FardK.Barbero LiñánM.115137SpringerBerlinSearch in Google Scholar
Murua, A., Sanz-Serna, J.M., (2018b), Hopf algebra techniques to handle dynamical systems and numerical integrators. In: E. Celledoni, G. di Nunno, K. Ebrahimi-Fard and H. Z. Munthe-Kaas (eds.) Computation and Combinatorics in Dynamics, Stocastics and Control, The Abel Symposium, Rosendal, August 2016, pp. 629-658. Springer, Berkub.MuruaA.Sanz-SernaJ.M.2018bHopf algebra techniques to handle dynamical systems and numerical integratorsCelledoniE.di NunnoG.Ebrahimi-FardK.Munthe-KaasH. Z.Computation and Combinatorics in Dynamics, Stocastics and ControlAugust2016629658SpringerBerkubSearch in Google Scholar
Sanders, J.A., Verhulst, F., and Murdock, J., (2007), Averaging Methods in Nonlinear Dynamical Systems (2nd. ed.). Springer, New York.SandersJ.A.VerhulstF.MurdockJ.20072ndSpringerNew YorkSearch in Google Scholar
Sanz-Serna, J.M., Murua, A., (2015), Formal series and numerical integrators: some history and some new techniques. In Lei-Guo and Zhiming-Ma (eds.) Proceedings of the 8th International Congress on Industrial and Applied Mathematics (ICIAM 2015), pp. 311-331. Higher Education, Press, Beijing.Sanz-SernaJ.M.MuruaA.2015Formal series and numerical integrators: some history and some new techniquesLei-GuoZhiming-Ma311331Higher Education, PressBeijingSearch in Google Scholar
Sanz-Serna, J.M., Zhu, Beibei, (2019), A stroboscopic averaging algorithm for highly oscillatory delay problems. IMA J. Numer. Anal. to appear (arXiv 1703.07300).Sanz-SernaJ.M.ZhuBeibei2019A stroboscopic averaging algorithm for highly oscillatory delay problemsSearch in Google Scholar