ode45 output incorrect - possible incorrect function definition?

Question

Jess 2014-5-25

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https://ww2.mathworks.cn/matlabcentral/answers/131070-ode45-output-incorrect-possible-incorrect-function-definition

回答： Star Strider 2014-5-25

I have two functions, one to define the differential equation and one to perform ode45 and solve the equation numerically. However, ode45 seems to give a very suspicious output which after solving the equation by hand I can see clearly that it is incorrect. I feel that I have somehow defined the equation incorrect but cannot see how. If possible could someone just have a once over the code to see if I am missing something anywhere, thanks.

Function to define the differential equation:

function dndt = productdiffeqn(t,n,par)
a = par(1);
m = par(2);
c = par(3);
dndt = ((a*10*(c-n))/(m+c-n));
end

Function to solve it:

function ndata = productsol(par, tyear)
n0 = 0;
[tdata,ndata] = ode45(@productdiffeqn,[tyear],n0,[],[par]);
tdata
end

Called with:

productsol([1,1,1],[tyear])
tdata =
       0
       1
       2
       3
       4
       6
      12
ans =
           0
      1.0007
      0.9995
      1.0000
      0.9991
      0.9994
      0.9999

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Star Strider 2014-5-25

What differential equation did you start with?

We need to know that and other details of what you’re doing before we can figure out what’s wrong.

Jess 2014-5-25

编辑：Jess 2014-5-25

dn/dt = (10a(c-n))/(m+c-n)

Constants a,c,m are all >0. Initial value of n: n(0) = 0.

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Answer 1

Star Strider 2014-5-25

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The constants a, c, and m all have to be in your workspace, but you can solve your ODE with an anonymous function:

c = 1;
m = 5;
a = 7;
productdiffeqn = @(t,n) (10.*a.*(c-n))./(m+c-n);
tyear = [0 1 2 3 4 6 12];
n0 = 0;
[t, n] = ode45(productdiffeqn, tyear, n0);
figure(1)
plot(t, n)
grid