Difference between revisions of "Final2018"
(Created page with "The final project for the 2018 Intro. Scientific Computing is to reproduce all 15 figures from the paper, ``Stability and Hopf bifurcations in an inverted pendulum'' by Blackb...") |
|||
| Line 1: | Line 1: | ||
| − | The final project for the 2018 Intro. Scientific Computing is to reproduce all 15 figures from the paper, |
+ | The final project for the 2018 Intro. Scientific Computing is to reproduce all 15 figures from the paper, "Stability and Hopf bifurcations in an inverted pendulum" by Blackburn, Smith, and Grønbeck-Jensen [https://aapt.scitation.org/doi/10.1119/1.17011]. |
Each student must hand in their own solutions for this project, but discussion groups of any size are encouraged. |
Each student must hand in their own solutions for this project, but discussion groups of any size are encouraged. |
||
Note that there is an erratum published for this paper stating that the captions for Figures 5,6, and 7 were mis-placed. Caption 5 goes with Fig. 7, Caption 6 goes with Fig. 5, and Caption 7 goes with Fig. 6. |
Note that there is an erratum published for this paper stating that the captions for Figures 5,6, and 7 were mis-placed. Caption 5 goes with Fig. 7, Caption 6 goes with Fig. 5, and Caption 7 goes with Fig. 6. |
||
| − | Although you can use scipy's odeint, it is more appropriate to reproduce the data using the 4th order Runge-Kutta method that the original authors used. |
+ | Although you can use scipy's odeint, it is more appropriate to reproduce the data using the 4th order Runge-Kutta method that the original authors used. It is implemented in [https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.RK45.html#scipy.integrate.RK45 scipy.integrate.RK45]. There is still a slight difference, since the above will use a variable time-step while the original authors used a fixed time-step. Variable time-step methods are generally better but have a different way of setting the acceptable integration error. |
| − | |||
| − | from scipy.integrate import ode |
||
| − | r = ode(f, jac).set_integrator('dopri5', method='bdf') |
||
| − | ode.set_integrator("dopri5") |
||
| − | |||
| − | before using '''scipy.integrate.ode''' [https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.ode.html]. There is still a slight difference, since the above will use a variable time-step while the original authors used a fixed time-step. Variable time-step methods are generally better but have a different way of setting the acceptable integration error. |
||
Revision as of 11:31, 27 March 2018
The final project for the 2018 Intro. Scientific Computing is to reproduce all 15 figures from the paper, "Stability and Hopf bifurcations in an inverted pendulum" by Blackburn, Smith, and Grønbeck-Jensen [1]. Each student must hand in their own solutions for this project, but discussion groups of any size are encouraged.
Note that there is an erratum published for this paper stating that the captions for Figures 5,6, and 7 were mis-placed. Caption 5 goes with Fig. 7, Caption 6 goes with Fig. 5, and Caption 7 goes with Fig. 6.
Although you can use scipy's odeint, it is more appropriate to reproduce the data using the 4th order Runge-Kutta method that the original authors used. It is implemented in scipy.integrate.RK45. There is still a slight difference, since the above will use a variable time-step while the original authors used a fixed time-step. Variable time-step methods are generally better but have a different way of setting the acceptable integration error.
