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headmyshoulder / odeint-v2

odeint - solving ordinary differential equations in c++ v2
http://headmyshoulder.github.com/odeint-v2/
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multiprecision enabled symplectic stepper #43

Closed mariomulansky closed 11 years ago

mariomulansky commented 12 years ago

The current high-order symplectic stepper is not suitable for high-precision types as it constructs parameters from double. A symplectic stepper with arguments constructed from integers should be added, i think such a stepper can be found e.g. in R. McLachlan: "ON THE NUMERICAL INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS BY SYMMETRIC COMPOSITION METHODS" , 1995

headmyshoulder commented 12 years ago

Hmm, for the current stepper the formulas for the construction of a1, and a2 are not given in this paper.

headmyshoulder commented 12 years ago

Implement SB3A with m=4. Here, all coefficients are analytically known.

headmyshoulder commented 11 years ago

Done, tests have still to be implemented.