Work Package | Bibliographical details |
WP1 | Morten Dahlby, Brynjulf Owren and Takaharu Yaguchi, Preserving multiple first integrals by discrete gradients, J. Phys A 2011 |
WP1 | E. Celledoni, B. Owren Y. Sun. ``On energy preserving integrators for polynomial Hamiltonians’’, Workshop on Geometric Numerical Integration, March 20-24.Organized by: Ernst Hairer, Marlis Hochbruck, Arieh Iserles and Christian Lubich, Oberwolfach reports vol 8, issue 1, 2011. ISSN 1660-8933. |
WP1 | Morten Dahlby, Integral-preserving numerical methods for differential equations, PhD thesis, NTNU, November 2011. |
WP1 | S. Christiansen, H. Munthe-Kaas, B. Owren, Topics in structure-preserving discretization , Acta Numerica 2011. |
WP1 | E. Celledoni, R.I. McLachlan, B. Owren and G.R.W. Quispel, On conjugate B-series and their geometric structure, JNAIAAM 2011. |
WP1 | V. Grimm, R.I. McLachlan, D.I. McLaren, D.R.J. O'Neale, B. Owren, G.R.W. Quispel) Preserving energy resp. dissipation in numerical PDEs, using the "average vector field" method, arXiv:1202.4555v1. J. Comp Phys. |
WP1 | E Celledoni, B. Owren, Y Sun, The minimal stage, energy preserving Runge-Kutta method for polynomial Hamiltonian systems is the Averaged Vector Field method, arXiv:1203.3252v1 [math.NA], submitted. (D 1.2) |
WP2 | A. Zanna, ``Recent advancements on explicit volume-preserving splitting methods”, Workshop on Geometric Numerical Integration, March 20-24.Organized by: Ernst Hairer, Marlis Hochbruck, Arieh Iserles and Christian Lubich, Oberwolfach reports vol 8, issue 1, 2011. ISSN 1660-8933. |
WP2 | H. Xue, A. Zanna, ``Explicit volume-preserving splitting methods for polynomial divergence-free vector fields’’. BIT, Numerical Mathematics (2013). |
WP2 | A. Zanna: "The Euler equations of quasi-geostrophic fluids and volume-preserving numerical methods" Report University of Bergen. |
WP3 | Alexander Lundervold, Hans Munthe-Kaas, Backward error analysis and the substitution law for Lie group integrators, arXiv:1106.1071v1, oundations of Computational Mathematics. 13: 161-186. 2012-07-10. doi: 10.1007/s10208-012-9130-z |
WP3 | Alexander Lundervold, Hans Z. Munthe-Kaas, On algebraic structures of numerical integration on vector spaces and manifolds, arXiv:1112.4465v1 |
WP3 | Kurusch Ebrahimi-Fard, Alexander Lundervold, Simon J. A. Malham, Hans Munthe-Kaas, Anke Wiese, Algebraic structure of stochastic expansions and efficient simulation, arXiv:1112.5571v3 [math.NA]. Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. 468: 2361-2382. doi: 10.1098/rspa.2012.0024 |
WP3 | Hans Munthe-Kaas, Alexander Lundervold, On post-Lie algebras, Lie-Butcher series and moving frames, arXiv:1203.4738v1 Foundations of Computational Mathematics. 13: 583-613. doi: 10.1007/s10208-013-9167-7 |
WP3 | Alexander Lundervold, Lie–Butcher series and geometric numerical integration on manifolds, PhD thesis, November 2011 |
WP4 | M. Condon, A. Deaño, A. Iserles & K. Kropielnicka. "Efficient computation of delay differential equations with highly oscillatory terms". NA Report Cambridge. |
WP4 | M. J. Cantero & A. Iserles, "On rapid computation of expansions in ultraspherical polynomials". NA Report Cambridge. |
WP4 | M. J. Cantero & A. Iserles, "On expansions in orthogonal polynomials". NA Report Cambridge. |
WP4 | A. Boettcher, S. Grudsky & A. Iserles. "The Fox-Li operator as a test and a spur for Wiener-Hopf theory". NA Report Cambridge. |
WP4 | M. Condon, A. Deaño & A. Iserles, "A new simulation technique for RF oscillators". NA Report Cambridge. |
WP4 | M. J. Cantero & A. Iserles, "Orthogonal polynomials on the unit circle and functional-differential equations".NA Report Cambridge. |
WP4 | M. J. Cantero & A. Iserles, "On a curious q-hypergeometric identity".NA Report Cambridge. |
WP4 | M. Condon, A. Deaño, J. Gao & A. Iserles, "Asymptotic solvers for ordinary differential equations with multiple frequencies". NA Report Cambridge. |
WP4 | S. Altinbasak, M. Condon, A. Deaño & A. Iserles, "Highly oscillatory diffusion-type equations". NA Report Cambridge. |
WP4 | A. Iserles & K. Kropielnicka "Effective approximation for linear time-dependent Schrödinger equation". NA Report Cambridge. |
WP4 | M. Dahlby and B. Owren, A general framework for deriving integral preserving numerical methods for PDEs, SIAM J. Sci. Comp. 2011, vol 33. |
WP4 | R.I McLachlan, Some topics in multisymplectic integration, Oberwolfach Report 16/2011, pp. 14-17. DOI: 10.4171/OWR/2011/16 |
WP4 | A. Zanna, ``Generalized Polar Decompositions in Control’’. Textos de matemática : mathematical papers in honour of Fátima Silva Leite. Coimbra: Universidade de Coimbra 2011 ISBN 978-972-8564-47-6. s. 123-134. |
WP1 | E. Celledoni, B. Owren and Y. Sun, `` The minimal stage, energy-preserving Runge-Kutta method for polynomial Hamiltonian systems is the Averaged vector Fiels method." arXiv:1203.3252v1. Math. Comp. |
WP1 | E. Celledoni, H. Marthinsen and B. Owren, `Àn introduction to Lie group integrators - basics, new developments and applicstions". arXiv:1207.0069. JCP.|
| WP2|A. Zanna, The Euler equation of quasi-geostrophic fluids and volume preserving numerical methods, arXiv:1205.1947v1|
| WP1/2| E. Celledoni, R.I. McLachlan, B. Owren, GWR Quispel, Geometric properties of Kahan's method. J Phys. A |
| WP1 |E. Celledoni, B. Owren, ``Preserving first integrals with symmetric Lie group methods´´, DCDS A (2014). |
WP2 | H. Xue and A. Zanna, "GENERATING FUNCTIONS AND VOLUME PRESERVING MAPPINGS", DCDS A (2014). |
WP1 | RI McLachlan and R. Quispel, "Discrete gradient methods have an energy conservation law", DCDS A (2014) |
WP3 | F. Bartha and H. Munthe-Kaas, "COMPUTING OF B-SERIES BY AUTOMATIC DIFFERENTIATION", DCDS A (2014). |
WP2 | E. Celledoni, B.K. Kometa and O. Verdier, High-order semi-Lagrangian methods for the incompressible Navier-Stokes equations, arXiv:1207.5147v1, J Sci Comp.(2015) |
WP4 | E. Celledoni, E.H. Hoiseth and N. Ramzina, Splitting methods for controlled vessel marine operations, submitted. (2014) |
WP4 | E. Celledoni, RI McLachlan, D. McLaren, B. Owren and GWR Quispel, Integrability properties of Kahan's method arXiv: 1405.3740, J. Phys A. (2014) |
WP4 | S. Blanes & A. Iserles, "Explicit adaptive symplectic integrators for solving Hamiltonian systems" Celestial Mech. & Dynamical Astronomy 114 (2012) 297–317. |
WP4 | M. Condon, A. Deaño, J. Gao & A. Iserles, "Asymptotic solvers for second-order differential equation systems with multiple frequencies" Calcolo 51 (2014), 109–139. |
WP4 | M. J. Cantero & A. Iserles, "On expansions in orthogonal polynomials", Adv. Comp. Maths 38 (2013), 35–61. |
WP4 | A. Iserles, "On skew-symmetric differentiation matrices", IMA J. Num. Anal. 34 (2014), 435–451. |
WP4 | S. Altinbasak Üsküplu, M. Condon, A. Deaño & A. Iserles, "Highly oscillatory diffusion-type equations", J. Comp. Maths. 31 (2014), 549–572. |
WP4 | M. Condon, A. Iserles & S.P. Nørsett, "Differential equations with general highly oscillatory forcing terms" , Proc. Royal Soc. A 470 (2014). |
WP4 | B. Wang & A. Iserles, "Dirichlet series for dynamical systems of first-order ordinary differential equations", Disc. & Cont. Dynamical Sys. B 19 (2014), 281–298. |
WP4 | P. Bader, A. Iserles, K. Kropielnicka & P. Singh, "Effective approximation for the linear time-dependent Schrödinger equation", to appear in Found. Comp. Maths. |
WP4 | Bin Wang, Arieh Iserles & Xinyuan Wu, "Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems", to appear in Found. Comp. Maths. |
WP4 | M. J. Cantero & A. Iserles, "From orthogonal polynomials on the unit circle to functional equations via generating functions" to appear in Transactions Amer. Maths Soc.. |
WP4 | A.G.C. P. Ramos & A. Iserles, "Numerical solution of Sturm–Liouville problems via Fer streamers" to appear in Numerische Mathematik. |
WP4 | E. Hairer & A. Iserles, "Numerical stability in the presence of variable coefficients" to appear in Found. Comp. Maths. |
WP2 | H Marthinsen and B. Owren, "Geometric integration of non-autonomous Hamiltonian problems ", arXiv:1409.5058, to appear in Num. Algs. |
WP3 | O. Verdier, H. Munthe-Kaas, Aromatic Butcher Series. Foundations of Computational Mathematics. doi: 10.1007/s10208-015-9245-0, (2015). |
WP4 | H. Munthe-Kaas, Hans, GRW Quispel, A. Zanna, 2014. Symmetric spaces and Lie triple systems in numerical analysis of differential equations. BIT Numerical Mathematics. 54: 257-282. doi: 10.1007/s10543-014-0473-5. |
WP1 | RA Norton, DI McLaren, GRW Quispel, A Stern, A. Zanna, 2015. Projection methods and discrete gradient methods for preserving first integrals of ODES. Discrete and Continuous Dynamical Systems. 35: 2079-2098. |
WP4 | E. Celledoni, JM Sanz-Serna, A. Zanna, 2014. Guest editors' preface. Discrete and Continuous Dynamical Systems. 34: i-ii. doi: doi:10.3934/dcds.2014.34.3i |
WP4 | S Marsland, R McLachlan, K Modin, and M Perlmutter, On conformal variational problems and free boundary continua, J. Phys. A 47 (2014) 145204 |
WP2 | R I McLachlan, K Modin, and O Verdier, Collective symplectic integrators, Nonlinearity 27(6) (2014), 1525-1542. |
WP2 | R I McLachlan, K Modin, and O Verdier, Collective Lie-Poisson integrators on R3, IMA J. Numer. Anal. (2014). |
WP4 | R I McLachlan and A Stern, Modified trigonometric integrators, SIAM J. Numer. Anal. 52(3) (2014), 1378-1397. |
WP2 | R I McLachlan, K Modin, O Verdier, and M Wilkins, Geometric generalisations of SHAKE and RATTLE, Foundations of Computational Mathematics 14 (2014), 339-370. |
WP2 | R I McLachlan, K Modin, and O Verdier, Symplectic integrators for spin systems, Phys. Rev. E . |
WP2 | R I McLachlan, K Modin, and O Verdier, Discrete time Hamiltonian spin systems, 2014. |
WP1 | R.A. Norton and G.R.W. Quispel, ‘Discrete gradient methods for preserving a first integral of an ordinary differential equation’, Discrete and Continuous Dynamical Systems, 34 (2014), 1147-1170. |
WP3 | HS Sundklakk, A library for computing with trees and B-series, specialization project, NTNU, 2014, https://github.com/henriksu/pybs |