Found 110 Documents (Results 1–100)
Validated B-series and Runge-Kutta pairs. (English) Zbl 07869106
MSC:
65-XX
Using aromas to search for preserved measures and integrals in Kahan’s method. (English) Zbl 07833091
Reviewer: William J. Satzer Jr. (St. Paul)
Computing with B-series. (English) Zbl 07910028
MSC:
65-XX
Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds. (English) Zbl 1487.60112
A novel way constructing symplectic stochastic partitioned Runge-Kutta methods for stochastic Hamiltonian systems. (English) Zbl 07907264
From Runge-Kutta methods to Hopf algebras of rooted trees. (English) Zbl 1493.16031
Makhlouf, Abdenacer (ed.), Algebra and applications 2. Combinatorial algebra and Hopf algebras. London: ISTE; Hoboken, NJ: John Wiley & Sons. Sciences, 179-219 (2021).
Energy-preserving exponential integrators of arbitrarily high order for conservative or dissipative systems with highly oscillatory solutions. (English) Zbl 07513793
Some drift exponentially fitted stochastic Runge-Kutta methods for solving Itô SDE systems. (English) Zbl 1431.65105
Trees and B-series. (English) Zbl 1480.65163
Explicit integrator of Runge-Kutta type for direct solution of \(u^{(4)} = f(x, u, u', u'')\). (English) Zbl 1416.65203
MSC:
65L06
Trigonometrically fitted two-derivative Runge-Kutta-Nyström methods for second-order oscillatory differential equations. (English) Zbl 1477.65110
Hybrid methods for direct integration of special third order ordinary differential equations. (English) Zbl 1426.65089
MSC:
65L05
The geometry of characters of Hopf algebras. (English) Zbl 1450.16021
Celledoni, Elena (ed.) et al., Computation and combinatorics in dynamics, stochastics and control. The Abel symposium, Rosendal, Norway, August 16–19, 2016. Selected papers. Cham: Springer. Abel Symp. 13, 159-185 (2018).
General order conditions for stochastic partitioned Runge-Kutta methods. (English) Zbl 1394.65005
Reviewer: Melvin D. Lax (Long Beach)
An improved tri-coloured rooted-tree theory and order conditions for ERKN methods for general multi-frequency oscillatory systems. (English) Zbl 1376.65106
Order conditions for stochastic Runge-Kutta methods preserving quadratic invariants of Stratonovich SDEs. (English) Zbl 1375.65002
Erratum to: “Higher-order averaging, formal series and numerical integration. II: The quasi-periodic case”. (English) Zbl 1418.34097
Cheap arbitrary high order methods for single integrand SDEs. (English) Zbl 1364.65012
Reviewer: Melvin D. Lax (Long Beach)
Hamiltonian B-series and a Lie algebra of non-rooted trees. (English) Zbl 1368.65256
Reviewer: Fernando Casas (Castellon)
Multi-step Runge-Kutta-Nyström methods for special second-order initial value problems. (English) Zbl 1355.65097
The tame Butcher group. (English) Zbl 1408.22024
A technique for studying strong and weak local errors of splitting stochastic integrators. (English) Zbl 1353.65004
Flexible exponential integration methods for large systems of differential equations. (English) Zbl 1341.65027
Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method. (English) Zbl 1382.65206
MSC:
65L06
Convergence analysis of the formal energies of symplectic methods for Hamiltonian systems. (English) Zbl 1350.65138
Reviewer: Seenith Sivasundaram (Daytona Beach)
Aromatic Butcher series. (English) Zbl 1368.65113
Reviewer: Raffaella Pavani (Milano)
Structure-preserving algorithms for oscillatory differential equations II. (English) Zbl 1352.65187
Berlin: Springer; Beijing: Science Press (ISBN 978-3-662-48155-4/hbk; 978-3-662-48156-1/ebook). xv, 298 p. (2015).
Reviewer: Roland Pulch (Greifswald)
Order conditions for G-symplectic methods. (English) Zbl 1338.65185
Reviewer: Fernando Casas (Castellon)
Two-derivative Runge-Kutta-Nyström methods for second-order ordinary differential equations. (English) Zbl 1335.65059
Reviewer: Martin Reißel (Aachen)
Runge-Kutta methods for ordinary differential equations. (English) Zbl 1330.65109
Al-Baali, Mehiddin (ed.) et al., Numerical analysis and optimization. Selected papers based on the presentations at the 3rd international conference, NAO-III, Muscat, Oman, January 5–9, 2014. Cham: Springer (ISBN 978-3-319-17688-8/hbk; 978-3-319-17689-5/ebook). Springer Proceedings in Mathematics & Statistics 134, 37-58 (2015).
A new class of split exponential propagation iterative methods of Runge-Kutta type (sEPIRK) for semilinear systems of odes. (English) Zbl 1349.65227
A simplified Nyström-tree theory for extended Runge-Kutta-Nyström integrators solving multi-frequency oscillatory systems. (English) Zbl 1348.65110
Numerical integration of Hamiltonian problems by G-symplectic methods. (English) Zbl 1301.65127
Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)
The minimal stage, energy preserving Runge-Kutta method for polynomial Hamiltonian systems is the averaged vector field method. (English) Zbl 1296.65182
Reviewer: Fernando Casas (Castellon)
Direct integrators of Runge-Kutta type for special third-order ordinary differential equations. (English) Zbl 1285.65047
MSC:
65L06
Exponential B-series: the stiff case. (English) Zbl 1285.65043
Reviewer: Manuel Calvo (Zaragoza)
On post-Lie algebras, Lie-Butcher series and moving frames. (English) Zbl 1327.17001
Found. Comput. Math. 13, No. 4, 583-613 (2013); correction ibid.19, No. 1, 241 (2019).
On conjugate symplecticity of B-series integrators. (English) Zbl 1329.65307
Reviewer: Yajuan Sun (Beijing)
MSC:
65P10
Structure-preserving algorithms for oscillatory differential equations. (English) Zbl 1276.65041
Berlin: Springer; Beijing: Science Press (ISBN 978-3-642-35337-6/hbk; 978-3-642-35338-3/ebook). xii, 236 p. (2013).
Reviewer: Roland Pulch (Greifswald)
Higher-order averaging, formal series and numerical integration. II: The quasi-periodic case. (English) Zbl 1257.34031
Found. Comput. Math. 12, No. 4, 471-508 (2012); erratum ibid. 17, No. 2, 625-626 (2017).
On extended RKN integrators for multidimensional perturbed oscillators with applications. (English) Zbl 1243.65088
MSC:
65L06
A formal series approach to averaging: exponentially small error estimates. (English) Zbl 1246.34043
Subquadrature expansions for TSRK methods. (English) Zbl 1251.65106
Reviewer: Andrea Walther (Paderborn)
A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK). (English) Zbl 1370.65035
B-series analysis of iterated Taylor methods. (English) Zbl 1234.65018
Reviewer: Jialin Hong (Beijing)
Composition of stochastic B-series with applications to implicit Taylor methods. (English) Zbl 1208.65014
MSC:
65C30
ERKN integrators for systems of oscillatory second-order differential equations. (English) Zbl 1217.65141
MSC:
65L05
Higher-order averaging, formal series and numerical integration. I: B-series. (English) Zbl 1211.34052
Reviewer: Oleg Anashkin (Simferopol)
Energy-preserving integrators and the structure of B-series. (English) Zbl 1205.65325
Reviewer: Werner M. Seiler (Kassel)
Algebraic structures of B-series. (English) Zbl 1201.65124
Reviewer: Seenith Sivasundaram (Daytona Beach)
Stochastic Taylor expansions: Weight functions of B-series expressed as multiple integrals. (English) Zbl 1188.65005
Reviewer: Kevin Burrage (Brisbane)
Ramification of rough paths. (English) Zbl 1315.60065
Symplectic geometric algorithms for Hamiltonian systems. With a foreword by Feng Duan and a preface by Qin, Mengzhao. (English) Zbl 1207.65149
Hangzhou: Zhejiang Publishing United Group, Zhejiang Science and Technology Publishing House; Berlin: Springer (ISBN 978-7-5341-3595-8; 978-3-642-01776-6/hbk). xxiii, 676 p. (2010).
Reviewer: Kevin Burrage (Brisbane)
Note on derivation of order conditions for ARKN methods for perturbed oscillators. (English) Zbl 07872398
B-series analysis of stochastic Runge-Kutta methods that use an iterative scheme to compute their internal stage values. (English) Zbl 1188.65006
Reviewer: Melvin D. Lax (Long Beach)
On multidimensional ARKN methods for systems of perturbed oscillators. (English) Zbl 1185.65128
Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics, Rethymno, Crete, Greece, September 18–22, 2009. Vol. 2. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0708-4/hbk; 978-0-7354-0709-1/set). AIP Conference Proceedings 1168, 2, 896-899 (2009).
Structure of B-series for some classes of geometric integrators. (English) Zbl 1182.65189
Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics, Rethymno, Crete, Greece, September 18–22, 2009. Vol. 2. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0708-4/hbk; 978-0-7354-0709-1/set). AIP Conference Proceedings 1168, 2, 739-742 (2009).
B-series and B-series coefficients. (English) Zbl 1182.65112
Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics 2009, Rethymno, Crete, Greece, September 18–22, 2009. Vol. 1. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0705-3/hbk; 978-0-7354-0709-1/set). AIP Conference Proceedings 1168, 1, 7-10 (2009).
Mirror principle for flag manifolds. (English) Zbl 1213.14090
Reviewer: Victor Przyjalkowski (Moskva)
Preserving first integrals and volume forms of additively split systems. (English) Zbl 1118.65086
Reviewer: Narahari Parhi (Bhubaneswar)
Conjugate symplecticity of second-order linear multi-step methods. (English) Zbl 1124.65060
Reviewer: Rudolf Scherer (Karlsruhe)
Expansions of step-transition operators of multi-step methods and order barriers for Dahlquist pairs. (English) Zbl 1105.65081
Reviewer: M. Gousidou-Koutita (Thessaloniki)
An algebraic approach to invariant preserving integators: the case of quadratic and Hamiltonian invariants. (English) Zbl 1100.65115
Reviewer: Werner M. Seiler (Kassel)
Order conditions for commutator-free Lie group methods. (English) Zbl 1095.65063
Reviewer: Alois Steindl (Wien)
B-series and order conditions for exponential integrators. (English) Zbl 1109.65060
Reviewer: Roland Pulch (Wuppertal)
Order conditions for a general family of two step nonlinear methods for \(y''= f(x,y)\). (English) Zbl 1136.65069
Runge-Kutta methods adapted to the numerical integration of oscillatory problems. (English) Zbl 1057.65043
Reviewer: R. Militaru (Craiova)
Order conditions for a class of two-step methods for \(y''=f(x,y)\). (English) Zbl 1022.65080
Reviewer: Dana Petcu (Timişoara)
Pre-Lie algebras and Hopf algebras related to renormalization. (Algèbres pré-Lie et algèbres de Hopf liées à la renormalisation.) (French) Zbl 0999.16027
Reviewer: B.Fauser (Tübingen)
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