Dealing with parasitic behaviour in G-Symplectic integrators

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

Volumn 120, Issue , 2013, Pages 105-123

  Butcher, J C ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

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EID: 84868566589     PISSN: 16122909     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-33221-0_7     Document Type: Conference Paper

References (11)

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2. Butcher, J.C.:Numerical Methods for Ordinary Differential Equations.Wiley, Chichester and New York (2008)
3. Butcher, J.C., Hewitt, L.L.: The existence of symplectic general linear methods. Numerical Algorithms 51, 77-84 (2009)
4. Butcher, J.C., Habib, Y., Hill, A.T., Norton, T.: Control of parasitism in G-symplectic methods (in preparation, 2012)
5. Butcher, J.C., Hill, A.T.: Symmetric general linear methods (in preparation, 2012)
6. Dahlquist, G.: Error analysis for a class of methods for stiff non-linear initial value problems. Lecture Notes in Mathematics, vol. 506, pp. 60-72 (1976)
7. Cooper, G.J.: Stability of Runge-Kutta methods for trajectory problems. IMA J. Numer. Anal. 7, 1-13 (1987)
8. Hammer, P.C., Hollingsworth, J.W.: Trapezoidal methods of approximating solutions of differential equations. MTAC 9, 92-96 (1955)
9. Heun, K.: Neue Methoden zur approximativen Integration der Differentialgleichungen einer unabhängigen Veränderlichen. Z. Math. Phys. 45, 23-38
10. Kutta, W.: Beitrag zur näherungsweisen Integration totaler Differentialgleichungen. Z. Math. Phys. 46, 435-453 (1901)
11. Runge, C.: Über die numerische Auflösung von Differentialgleichungen. Math. Ann. 46, 167-178 (1895)