Explore BrainMass
Share

Explore BrainMass

    Matlab: Runge-Kutta versus Euler in a Lottka-Volterra example

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

    See the attached file.

    Consider the Lotka-Volterra system. Consider the following system of differential equations
    dx/dt=-x(2-y),t_0=0,x(t_0=1), (2)
    dy/dt=y(1-2x),t_0=0,y(t_0 )=2, (3)
    Let [0; 40] be the interval of integration.
    C1. Implement Runge-Kutta integration scheme with Δ = 0:005 for system (2), (3).Plot the phase curves (trajectories x(t); y(t) in the phase/state space).
    C2. Run explicit Euler and improved Euler integration schemes for the same system and same Δ. Plot the phase curves.
    How the results compare with the curves obtained using the Runge-Kutta method?

    © BrainMass Inc. brainmass.com October 10, 2019, 7:18 am ad1c9bdddf
    https://brainmass.com/computer-science/matlab/matlab-runge-kutta-euler-lottka-volterra-example-576288

    Attachments

    Solution Preview

    An example of a Matlab script to calculate and plot the three solutions on the same plot is attached.

    There is a difficulty in making all the three ...

    Solution Summary

    We arrange Matlab script to solve an example of Lottka-Volterra equations numerically, using either Runge-Kutta or two versions of Euler methods, and compare the three types of numerical solutions by plotting the results in the phase space.

    $2.19