MATLAB: Second order ODE15s going to infinity

differential equationodeode15ssecond order differential equationsecond order ode

Where μ = 1200, t is from 0 to 7000, and ODE15s is to be used.
tfinal = 7000;
delta_t = 0.01;
t = [0:delta_t:tfinal];
initial = [1 1];  % initial conditions
[t,w] = ode15s(@sub2,t,initial);    % line with error
figure
plot(t,w,'LineWidth',2)    
%%%%%%%%%% Subfunction
function d_dt = sub2(t,w)
 
mu = 1200;
% turning d^2y/dt^2 = mu(1-y^2)dydt - y     into     dzdt = mu(1-y)^2 - y
%                                                    dydt = z
z = w(1);  
y = w(2);
d_dt = zeros(2, 1); % initialize the column vector of equations
d_dt(1,1) = mu*z*(1-y)^2 - y;  % first equation
d_dt(2,1) = z;  % second equation
end
I made the code above, but i keep getting the error: 
Warning: Failure at t=1.702777e-01.  Unable to meet integration tolerances without reducing the step size below the
smallest value allowed (4.440892e-16) at time t. 
> In ode15s (line 730)
  In sec_ord_diff (line 5)
I think it has something to do with μ being too large, or maybe the time step is too small/ big. Can anyone help me fix the issue? Thank you

Best Answer

Your ‘sub2’ function is not correct. 
sub2 = @(t,w,mu) [w(2); w(1)-mu*(w(1)^2-1)*w(2)];
mu = 1200;
tfinal = 7000;
delta_t = 0.1;
t = [0:delta_t:tfinal];
initial = [1 1];  % initial conditions
[t,w] = ode15s(@(t,w)sub2(t,w,mu),t,initial);    % line with error
figure
semilogy(t,w,'LineWidth',2)
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