Question

Problem 8 [5 points The following system of ODEs, formulated by Lorenz, represents are crude model of atmospheric circulation: Set σ-10, b = 8/3, r 28, take initial values yi (0) 15, 32(0) 15, and y3(0) 36, and integrate this ODE from t 0 to t 100 using Matlab's ode45. Plot each component of the solution as a function of t. Plot also (yi,2), (Ji. U3), and (2,y3) in separate plots). Change the initial values by a tiny amount (e.g. 10-10) and integrate again. Compare the difference in the computed solutions

Answer 1

In MATLAB:

function yp = programa (t,y)

y1=15;

y2=15;

y3=36

yp1=10*(y2-y1);

yp2=28*y1-y2-y1*y3;

yp3=y1*y2-(8/3)*y3;

yp=[yp1;yp2;yp3];

create new script with the following:

[t,y]= ode45(@programa, [0,100], [1,4]); #(change the initial values)

plot (t,y (:,1), t,y(:,2)); #(change for (y1,y3) and (y2,y3))

grid on

title (exercise);

xlabel(´t´);

xlabel(´y´);