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spin:esc201_hs2021 [2021/10/18 14:09] stadel [Lectures] |
spin:esc201_hs2021 [2021/10/25 14:06] sebastian [List of assignments] |
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- Fractals: Draw some Julia sets with various constants c (you can start with the Mandelbrot set as it was explained in the lecture and the exercise class)! (**to submit by 24 October, 2021, 9pm**) | - Fractals: Draw some Julia sets with various constants c (you can start with the Mandelbrot set as it was explained in the lecture and the exercise class)! (**to submit by 24 October, 2021, 9pm**) | ||
- Ordinary Differential Equations: Solve the Lotka-Volterra equation using the Euler method and the midpoint Runge-Kutta method (optional: 4th order Runge Kutta method) and compare the results. Make two plots: the time dependence of both populations (mice and foxes), and the phase diagram using different initial conditions (**to submit by 31 October, 2021, 9pm**). | - Ordinary Differential Equations: Solve the Lotka-Volterra equation using the Euler method and the midpoint Runge-Kutta method (optional: 4th order Runge Kutta method) and compare the results. Make two plots: the time dependence of both populations (mice and foxes), and the phase diagram using different initial conditions (**to submit by 31 October, 2021, 9pm**). | ||
+ | - Symplectic Integrators: Use the Leap-Frog method to make a phase plot (p vs q) of the harmonic oscillator for different total energies. Compare the results with what you get using the Forward Euler method and the midpoint Runge-Kutta method. Make the same plot for a simple pendulum (**to submit by 7 November, 2021, 9pm**). |