Often in astrodynamics we need conducting a high order integration of orbits in higly pertubed dynamics (the n-body problem augmented by the solar radiation pressure, J2, atmosphere, low-thrust, etc.). Some problems that I investigate require precise trajectory propagating. Does anybody know a very precise method of order, say, 30, 35, 40?
Hi, the precision of the integration can be achieved by any classical integrator (ode45, dopri8, etc...) with variable step. On output you will obtain the relative and absolute precisions you put on entry. When increasing the order of the integrator more calculus will be done at each step but the number of steps required to achieve a given precision will be lower. This is the only difference. Thus, if your problem is not stiff you can use any classical ode solver whatever the complexity of your dynamics.
If such high order is required, pseudo-spectral methods should be used.
Dear Maksim, Mathematica built-in internal function NDSolve has options for using adaptive embedded pairs of 2(1) through 9(8) Runge-Kutta methods; see attached document. Gianluca
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