Pseudo-symplectic Runge-Kutta Methods - Irisa

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5. Ь1А3с + Ь1{с.А2с) = brA2c. bT(c.A2c) + bT(Ac)2 = {bTc){bTAc). bTA2c2 + ٍT(cAc2) = bTAc2. bT{c.Ac2) + bT{c2.Ac) = {bTc2)(bTc). bT{c2.Ac) + bTA{c.Ac) = bT(c.
4 PS63 EXACT BUTCHER6

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Hamiltonian evolution for the kepler problem 2e-09 PS63 GAUSS4 GAUSS6

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Hamiltonian evolution for the kepler problem 1e-07 PS63 BUTCHER6 RADAU3 5e-08

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Error evolution for the kepler problem 0.01 PS63 GAUSS6 BUTCHER6 RADAU3 GAUSS4

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Diagram work-precision for the kepler problem 1 PS63 BUTCHER6 GAUSS4 GAUSS6 RADAU3

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Hamiltonian evolution for the bead problem 8e-07 PS63 GAUSS6 GAUSS4

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Hamiltonian evolution for the bead problem 6e-06 PS63 RADAU3 BUTCHER6

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Hamiltonian evolution for the modified pendulum problem 9e-05 GAUSS4 GAUSS6

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Hamiltonian evolution for the modified pendulum problem 0.002 PS63 RADAU3 BUTCHER6 0.0015

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Hamiltonian evolution for the galactic dynamic problem 0.001 PS63 BUTCHER6 RADAU3 0.0005

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Hamiltonian evolution for the galactic dynamic problem 0 PS63 GAUSS6 GAUSS4

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