Explore BrainMass

Explore BrainMass

    Euler, Improved Euler, and Runge Kutta for Lorenz attractor, and Butterfly Effect

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    In 1963 Edward Lorenz derived a simple set of equations describing convection in the atmosphere:

    See attached for equations.

    1. Please implement Euler integration scheme for (1) with integration step delta = 0.0001
    2. Please implement improved Euler integration scheme for (1) with delta = 0.0001
    3. Please implement Runge-Kutta integration scheme for (1)) with delta = 0.0001. Change x(0)=0 to x(0)=0.0001. Observe the butterfly effect.

    © BrainMass Inc. brainmass.com March 5, 2021, 1:19 am ad1c9bdddf


    Solution Preview

    The attached script shows an example of how the calculations for 1, 2, and 3 may be arranged.


    (1) To speed up the tests, I took delta_t and delta_x larger than that suggested in the text.
    When you arrive to the final ...

    Solution Summary

    In a Matlab script, we demonstrate the application of Euler, Improved Euler, and Runge Kutta numerical methods for Lorenz attractor, and the Butterfly Effect caused by a small change of initial conditions. The solution helps implement the Euler integration scheme and the Runge-Kutta integration scheme for various equations.