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

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?

#### 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.

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