Bader, Philipp; McLaren, David I.; Quispel, G. R. W.; Webb, Marcus Volume preservation by Runge-Kutta methods. (English) Zbl 1416.65509 Appl. Numer. Math. 109, 123-137 (2016). MSC: 65P10 65L06 PDFBibTeX XMLCite \textit{P. Bader} et al., Appl. Numer. Math. 109, 123--137 (2016; Zbl 1416.65509) Full Text: DOI arXiv
Munthe-Kaas, H. Z.; Quispel, G. R. W.; Zanna, A. Symmetric spaces and Lie triple systems in numerical analysis of differential equations. (English) Zbl 1291.65254 BIT 54, No. 1, 257-282 (2014). Reviewer: Walter Freyn (Augsburg) MSC: 65L99 53C35 58J70 34A26 PDFBibTeX XMLCite \textit{H. Z. Munthe-Kaas} et al., BIT 54, No. 1, 257--282 (2014; Zbl 1291.65254) Full Text: DOI arXiv
Celledoni, Elena; McLachlan, Robert I.; Owren, Brynjulf; Quispel, G. R. W. Energy-preserving integrators and the structure of B-series. (English) Zbl 1205.65325 Found. Comput. Math. 10, No. 6, 673-693 (2010). Reviewer: Werner M. Seiler (Kassel) MSC: 65P10 05C05 37M15 37C10 PDFBibTeX XMLCite \textit{E. Celledoni} et al., Found. Comput. Math. 10, No. 6, 673--693 (2010; Zbl 1205.65325) Full Text: DOI Link
Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. Reinout W.; Wright, William M. Energy-preserving Runge-Kutta methods. (English) Zbl 1169.65348 ESAIM, Math. Model. Numer. Anal. 43, No. 4, 645 (2009). MSC: 65P10 37M15 65L06 PDFBibTeX XMLCite \textit{E. Celledoni} et al., ESAIM, Math. Model. Numer. Anal. 43, No. 4, 645 (2009; Zbl 1169.65348) Full Text: DOI EuDML
McLachlan, R. I.; Munthe-Kaas, H. Z.; Quispel, G. R. W.; Zanna, A. Explicit volume-preserving splitting methods for linear and quadratic divergence-free vector fields. (English) Zbl 1147.65053 Found. Comput. Math. 8, No. 3, 335-355 (2008). MSC: 65L05 34A26 34C14 34A30 34A34 PDFBibTeX XMLCite \textit{R. I. McLachlan} et al., Found. Comput. Math. 8, No. 3, 335--355 (2008; Zbl 1147.65053) Full Text: DOI
Grimm, V.; Quispel, G. R. W. Geometric integration methods that preserve Lyapunov functions. (English) Zbl 1094.65070 BIT 45, No. 4, 709-723 (2005). Reviewer: Manuel Calvo (Zaragoza) MSC: 65L06 65P40 65L05 37M25 34A34 34A26 65L20 PDFBibTeX XMLCite \textit{V. Grimm} and \textit{G. R. W. Quispel}, BIT 45, No. 4, 709--723 (2005; Zbl 1094.65070) Full Text: DOI
Tuwankotta, J. M.; Quispel, G. R. W. Geometric numerical integration applied to the elastic pendulum at higher-order resonance. (English) Zbl 1107.37309 J. Comput. Appl. Math. 154, No. 1, 229-242 (2003). MSC: 37M15 65P10 70H08 70-08 PDFBibTeX XMLCite \textit{J. M. Tuwankotta} and \textit{G. R. W. Quispel}, J. Comput. Appl. Math. 154, No. 1, 229--242 (2003; Zbl 1107.37309) Full Text: DOI arXiv
Quispel, G. R. W.; McLaren, D. I. Explicit volume-preserving and symplectic integrators for trigonometric polynomial flows. (English) Zbl 1047.76103 J. Comput. Phys. 186, No. 1, 308-316 (2003). MSC: 76M25 65L05 65P10 PDFBibTeX XMLCite \textit{G. R. W. Quispel} and \textit{D. I. McLaren}, J. Comput. Phys. 186, No. 1, 308--316 (2003; Zbl 1047.76103) Full Text: DOI
Mclachlan, Robert I.; Quispel, G. R. W. Generating functions for dynamical systems with symmetries, integrals, and differential invariants. (English) Zbl 1194.37089 Physica D 112, No. 1-2, 298-309 (1998). MSC: 37J35 37K10 53D17 65L06 70-08 70H05 PDFBibTeX XMLCite \textit{R. I. Mclachlan} and \textit{G. R. W. Quispel}, Physica D 112, No. 1--2, 298--309 (1998; Zbl 1194.37089) Full Text: DOI
Quispel, G. R. W.; Dyt, C. P. Volume-preserving integrators have linear error growth. (English) Zbl 0945.65140 Phys. Lett., A 242, No. 1-2, 25-30 (1998). MSC: 65P10 34C25 65L70 37C27 37M15 PDFBibTeX XMLCite \textit{G. R. W. Quispel} and \textit{C. P. Dyt}, Phys. Lett., A 242, No. 1--2, 25--30 (1998; Zbl 0945.65140) Full Text: DOI