MATLAB: Ode45 returns NaN for a system of differential equations

differential equationsnanode45system of differential equations

I am attempting to generate two vectors, tv and Yv, to plot a series of differential equations. Given my funciton:
function dydt=Tcells(t,y)
dydt(1,1)=(10 + 0.03*y(1)*(1-y(1)/t) – 0.02*y(1) – (2.4e-5)*y(4)*y(1));
dydt(2,1)=(2.4e-5)*y(4)*y(1) – 0.02*y(2) – (3e-3)*y(2);
dydt(3,1)=(3e-3)*y(2) – 0.24*y(3);
dydt(4,1)=1400*y(3) – 2.4e-5*y(4)*y(1) – 2.4*y(4);
and the following ode45 script entry:
[tv, Yv]=ode45('Tcells',[0 1500],[500, 0, 0, 1000]);
I cannot figure out why all entries of Yv, save the first row, return NaN as their values.
Any and all help is appreciated.

Best Answer

Evan, the issue is the term
 (1-y(1)/t)
at t=0. If you set t0 for the integration time span slightly differently, such as
 [tv, Yv] = ode45('Tcells',[0.1 1500],[500, 0, 0, 1000]); % 0.1 instead of 0.0
you should get it to work. Also, to improve readability and performance (especially for more complex, non-linear ODEs):
 function dydt = Tcells(t,y)
 y1 = y(1);
 y2 = y(2);
 y3 = y(3);
 y4 = y(4);
 dydt = [10 + 0.03*y1*(1-y1/t) - 0.02*y1 - (2.4e-5)*y4*y1; ...
         (2.4e-5)*y4*y1 - 0.02*y2 - (3e-3)*y2; ...
         (3e-3)*y2 - 0.24*y3; ...
         1400*y3 - 2.4e-5*y4*y1 - 2.4*y4];
 end
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