Numerical long-term integration of geodesic equations of motion

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Numerical experimentsρ(0) = 30.7: regular motion400.1200.05z0ρ .0-20-0.050 10 20 30 40 50 60ρ30 40 50 60ρFigure: TrajectoryFigure: Sections at z = 016/26 | Jonathan Seyrich (Numerical long-term integration) Tübingen | January 21, 2013
Numerical experimentsρ(0) = 30.7: regular motion∆H(τ)1e-0121e-0131e-0141e-015RK5con, h=0.01RK5var, h=0.01CM2, ε=1, s=4CM1, ε=1, s=4IGEM, ε=1, s=4Integrator T calc [s]IGEM, ɛ = 1.0, s = 4 41.3RK5con, h = 0.01 222.9RK5var, h max = 0.01 160.6CM1, ɛ = 1.0, s = 4 17.3CM2, ɛ = 1.0, s = 4 46.10 100000 200000 300000 400000 500000τFigure: Energy error ∆H = | [H(yn)−H 0]/H 0 |.Table: CPU calculation times T calc17/26 | Jonathan Seyrich (Numerical long-term integration) Tübingen | January 21, 2013
Page 1 and 2: Numerical long-term integration of
Page 3 and 4: Problem and motivationGeodesic equa
Page 5 and 6: Numerical properties of the equatio
Page 11 and 12: Structure preserving integrator for
Page 13 and 14: Numerical experimentsTestcase: Mank
Page 15: Numerical experiments◮ We choose:
Page 19 and 20: Numerical experimentsρ(0) = 1.7:st
Page 21 and 22: Numerical experimentsρ(0) = 0.7: c
Page 23 and 24: Numerical experiments◮ IGEM calcu
Page 25 and 26: Summary◮ Energy conservation impo
Page 27: SummaryReferences II26/26 | Jonatha

Numerical long-term integration of geodesic equations of motion

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