Chartier, Philippe; Crouseilles, Nicolas; Lemou, Mohammed; Méhats, Florian Averaging of highly-oscillatory transport equations. (English) Zbl 1458.35036 Kinet. Relat. Models 13, No. 6, 1107-1133 (2020). MSC: 35B27 35Q49 82B40 35Q83 PDFBibTeX XMLCite \textit{P. Chartier} et al., Kinet. Relat. Models 13, No. 6, 1107--1133 (2020; Zbl 1458.35036) Full Text: DOI arXiv
Calvo, M. P.; Sanz-Serna, J. M.; Zhu, Beibei High-order stroboscopic averaging methods for highly oscillatory delay problems. (English) Zbl 1445.65023 Appl. Numer. Math. 152, 466-479 (2020). Reviewer: Zhanyuan Hou (London) MSC: 65L05 65P10 34E13 34E20 34C10 34C29 34C15 PDFBibTeX XMLCite \textit{M. P. Calvo} et al., Appl. Numer. Math. 152, 466--479 (2020; Zbl 1445.65023) Full Text: DOI arXiv
Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations. (English) Zbl 07161200 Found. Comput. Math. 20, No. 1, 1-33 (2020). MSC: 65L20 74Q10 35K15 PDFBibTeX XMLCite \textit{P. Chartier} et al., Found. Comput. Math. 20, No. 1, 1--33 (2020; Zbl 07161200) Full Text: DOI arXiv Link
Sanz-Serna, J. M.; Zhu, Beibei Word series high-order averaging of highly oscillatory differential equations with delay. (English) Zbl 1506.34097 Appl. Math. Nonlinear Sci. 4, No. 2, 445-454 (2019). MSC: 34K33 PDFBibTeX XMLCite \textit{J. M. Sanz-Serna} and \textit{B. Zhu}, Appl. Math. Nonlinear Sci. 4, No. 2, 445--454 (2019; Zbl 1506.34097) Full Text: DOI arXiv
Alamo, A.; Sanz-Serna, J. M. Word combinatorics for stochastic differential equations: splitting integrators. (English) Zbl 1476.60092 Commun. Pure Appl. Anal. 18, No. 4, 2163-2195 (2019). Reviewer: Nikolas Tapia (Berlin) MSC: 60H05 16T05 PDFBibTeX XMLCite \textit{A. Alamo} and \textit{J. M. Sanz-Serna}, Commun. Pure Appl. Anal. 18, No. 4, 2163--2195 (2019; Zbl 1476.60092) Full Text: DOI arXiv
Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles Highly oscillatory problems with time-dependent vanishing frequency. (English) Zbl 1411.74046 SIAM J. Numer. Anal. 57, No. 2, 925-944 (2019). MSC: 74Q10 65L20 74S30 PDFBibTeX XMLCite \textit{P. Chartier} et al., SIAM J. Numer. Anal. 57, No. 2, 925--944 (2019; Zbl 1411.74046) Full Text: DOI arXiv
Castella, F.; Chartier, Ph.; Sauzeau, J. A formal series approach to the center manifold theorem. (English) Zbl 1408.37053 Found. Comput. Math. 18, No. 6, 1397-1434 (2018). MSC: 37D10 34C45 05C05 PDFBibTeX XMLCite \textit{F. Castella} et al., Found. Comput. Math. 18, No. 6, 1397--1434 (2018; Zbl 1408.37053) Full Text: DOI Link
Chartier, Philippe; Lemou, Mohammed; Méhats, Florian Highly-oscillatory evolution equations with multiple frequencies: averaging and numerics. (English) Zbl 1380.34087 Numer. Math. 136, No. 4, 907-939 (2017). Reviewer: Kanakadurga Sivakumar (Chennai) MSC: 34E15 34A12 34C29 65L05 PDFBibTeX XMLCite \textit{P. Chartier} et al., Numer. Math. 136, No. 4, 907--939 (2017; Zbl 1380.34087) Full Text: DOI Link
Murua, A.; Sanz-Serna, J. M. Word series for dynamical systems and their numerical integrators. (English) Zbl 1369.34022 Found. Comput. Math. 17, No. 3, 675-712 (2017). MSC: 34A25 34C29 65L05 70H05 16T05 PDFBibTeX XMLCite \textit{A. Murua} and \textit{J. M. Sanz-Serna}, Found. Comput. Math. 17, No. 3, 675--712 (2017; Zbl 1369.34022) Full Text: DOI arXiv
Dumas, H. Scott; Meyer, Kenneth R.; Palacián, Jesús F.; Yanguas, Patricia Asymptotic stability estimates near an equilibrium point. (English) Zbl 1442.37072 J. Differ. Equations 263, No. 2, 1125-1139 (2017). Reviewer: Xiang Zhang (Shanghai) MSC: 37J25 70H11 PDFBibTeX XMLCite \textit{H. S. Dumas} et al., J. Differ. Equations 263, No. 2, 1125--1139 (2017; Zbl 1442.37072) Full Text: DOI
Bogfjellmo, Geir; Schmeding, Alexander The Lie group structure of the Butcher group. (English) Zbl 1366.22010 Found. Comput. Math. 17, No. 1, 127-159 (2017). Reviewer: Nicolai K. Smolentsev (Kemerovo) MSC: 22E65 65L06 58A07 16T05 PDFBibTeX XMLCite \textit{G. Bogfjellmo} and \textit{A. Schmeding}, Found. Comput. Math. 17, No. 1, 127--159 (2017; Zbl 1366.22010) Full Text: DOI arXiv
Murua, A.; Sanz-Serna, J. M. Vibrational resonance: a study with high-order word-series averaging. (English) Zbl 1432.34058 Appl. Math. Nonlinear Sci. 1, No. 1, 239-246 (2016). MSC: 34C29 34E05 70K30 PDFBibTeX XMLCite \textit{A. Murua} and \textit{J. M. Sanz-Serna}, Appl. Math. Nonlinear Sci. 1, No. 1, 239--246 (2016; Zbl 1432.34058) Full Text: DOI arXiv
Alamo, A.; Sanz-Serna, J. M. A technique for studying strong and weak local errors of splitting stochastic integrators. (English) Zbl 1353.65004 SIAM J. Numer. Anal. 54, No. 6, 3239-3257 (2016). MSC: 65C30 60H10 60H35 34F05 65L06 65L70 PDFBibTeX XMLCite \textit{A. Alamo} and \textit{J. M. Sanz-Serna}, SIAM J. Numer. Anal. 54, No. 6, 3239--3257 (2016; Zbl 1353.65004) Full Text: DOI arXiv
Murua, A.; Sanz-Serna, J. M. Computing normal forms and formal invariants of dynamical systems by means of word series. (English) Zbl 1334.34087 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 138, 326-345 (2016). MSC: 34C20 70H05 PDFBibTeX XMLCite \textit{A. Murua} and \textit{J. M. Sanz-Serna}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 138, 326--345 (2016; Zbl 1334.34087) Full Text: DOI arXiv
Condon, Marissa; Deaño, Alfredo; Gao, Jing; Iserles, Arieh Asymptotic solvers for ordinary differential equations with multiple frequencies. (English) Zbl 1331.65095 Sci. China, Math. 58, No. 11, 2279-2300 (2015). MSC: 65L05 34A34 34C10 PDFBibTeX XMLCite \textit{M. Condon} et al., Sci. China, Math. 58, No. 11, 2279--2300 (2015; Zbl 1331.65095) Full Text: DOI arXiv Link
Chartier, P.; Murua, A.; Sanz-Serna, J. M. Higher-order averaging, formal series and numerical integration. III: Error bounds. (English) Zbl 1322.34057 Found. Comput. Math. 15, No. 2, 591-612 (2015). MSC: 34C29 65L06 34D20 70H05 34A25 PDFBibTeX XMLCite \textit{P. Chartier} et al., Found. Comput. Math. 15, No. 2, 591--612 (2015; Zbl 1322.34057) Full Text: DOI Link