ode45 returns NaN for a system of differential equations?

Question

Evan 2014-2-22

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/118206-ode45-returns-nan-for-a-system-of-differential-equations

编辑： Mischa Kim 2014-2-22

采纳的回答： Mischa Kim

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.

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Answer 1

Mischa Kim 2014-2-22

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/118206-ode45-returns-nan-for-a-system-of-differential-equations#answer_125626

编辑：Mischa Kim 2014-2-22

在 MATLAB Online 中打开

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