Implement runge-kutta integration scheme with delta 0005

Question

Consider the Lotka-Volterra system ,Consider the following system of differential equations

dx/dt = -x(2-y),t₀ = 0, x(t_0=1), (2)

dy/dt = y(1-2x),t₀ = 0, y(t_0 )=2, (3)

Let [0; 40] be the interval of integration.

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).

Run explicit Euler and improved Euler integration schemes for the same system andsame Δ.Plot the phase curves.

How the results compare with the curves obtained using the Runge-Kutta method?

Answer 1

For the following differential equations system, you have to Implement Runge-Kutta method dx/dt = -x(2-y),t0 = 0, x(t_0=1), (2) dy/dt = y(1-2x),t0 = 0, y(t_0 )=2, (3) Assume that [0; 40] be the interval of integration. Implement the Runge-Kutta integration scheme by ? = 0:005 for the system (2),(3). Plot the phase curves (trajectories x(t); y(t) in the phase or state space).