MIT OpenCourseWare http://ocw.mit.edu 16.346 Astrodynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.Exercises 33 Obtain a numerical solution of the equations dx = y x(0)=0 dt 0 ≤ t ≤ 2 h =0.1 dy = x y(0)=1 dt using the Runge-Kutta-Nystr¨om algorithms of: 1. Order two with one evaluation Error 10−3 2. Order three with two evaluations Error 10−4 3. Order four with three evaluations Error 4 × 10−6 4. Order five with four evaluations Error 2 × 10−8 5. Order six with five evaluations Error 2 × 10−10 Note: The exact solution is x = sinh t and y = cosh t so you have the opportunity to compare your approximate solutions with the exact ones. You may want to experiment with the time-step h if you have the time and
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