Question

Matlab Code Please

The van der Pol equation is a second order ODE which is written as follows: 91 where μ > 0 is a scalar parameter. Rewrite this equation as a system of first-order ODEs and solve it using the Euler method for t E 10.2, where μ-1. Explain the physics behind vour numerical results.

Answer 1

mu=1;
dydt = @(t,y)[y(2); mu*(1-y(1)^2)*y(2)+y(1)];
%y(1) is y1, y(2) is d(y1)/dt
h=.1;%step size,change it accordingly
t=0:h:2;%from 0 to 2
n=length(t);
y=zeros(length(t),2);
y(1,:)=[1,0];%initial conditions put in the first index
for i=2:n
    term=y(i-1,:)+h*dydt(t(i-1),y(i-1,:))';%euler method
    y(i,:)=term;
end
figure
plot(t,y(:,1),t,y(:,2))
legend('y_1','y_1''(t)')
fprintf(' t           y(t)            dy/dt\n')
fprintf('%5.2f%15.5f%15.4f\n',[t;y'])

2 0 t00 6 8 8 2 8 4 1 8 4 6 1 9 7 1 1 195 d0000-2276460193928443 /000000098627986169372 yo-2345667899999987766 000064242675956624565 000002575152243779716 o o o o o o o o o 9 5 8 5 4 3 9 1 7 7 18 dt00-360518543333220862 2、( 0 0 0 0 0 1 1 2 2 3 4 5 6 7 8 9 0 1 1 2 3 V 012345678901234567890 000000000011111111112> C> 兵