MATLAB: Variable coefficient

variable coefficients

Hi, I have a system of 4 non linear ODEs. I solved them using ode15s and it worked perfectly. But i used constant coefficients at that time. Now I want to do the same thing when the coefficients are variable. Is there any built-in solver for variable coefficients? If yes, then how do i input the coefficients as functions of time? Any guidance/help will be appreciated. thanks!!!!

Best Answer

All the solvers can handle variable coefficients - they are completely ignorant of the details of the equations. All they require is a function that returns some f(t,y) (with the dimension of f being the same as the dimension of y).

But perhaps you mean that you want to pass the time-dependent coefficients as parameters?

Can you maybe clarify? Give an example?

Related Solutions

MATLAB: Variable coefficients-help needed please!!!

I redefined your code as:

function dy  =  funl12(t,y)
dy(1,1)  =  (k1(t).*(y(4)-y(1)).*y(3))./(y(2)+y(3)-1e-12) - k2(t).*y(1).*(y(2)./(y(2)+y(3)-1e-12)) ;
dy(2,1)  =  (mu(t).*(y(2).^n)/(K(t)^n+y(2).^n)).*exp((-y(1)).*k)-(k3(t).*y(1).*y(2))./(y(2)+y(3)-1e-12)-(d1(t)+gamma(t).*y(4)).*y(2);
dy(3,1)  =  (k3(t).*y(1).*y(2))./(y(2)+y(3)-1e-12)-(d2(t)+gamma(t).*y(4)).*y(3);
dy(4,1)  =  r(t).*y(4).*(1-(y(4)./(alpha(t).*(y(2)+y(3)-1e-12))));
      % Nested k1
      function y  =  k1(t)
          y   = [0.04226,0.1593,0.1460,0.1489];
          idx = logical(histc(t,[0,91.25,182.5,273.75,366]));
          y   = y(idx);
      end
      % Nested k2
      function y  =  k2(t)
          y   = [0.008460,0.04959,0.03721,0.04750];
          idx = logical(histc(t,[0,91.25,182.5,273.75,366]));
          y   = y(idx);
      end
  end

Remarks:

Histc uses the following boundary behavior low <= t < up and this is consistent with k(0). In your code k(0) didn't return any value, thus the error you got. In this case it returns 0.04226 (if k1) or 0.008460 (if k2). Note that to include 365 I shifted it to 366 (assuming you'll never have values bigger equal than 366).
Now I get an error on d(1,2) because I don't have code for K, k, gamma etc..
No need to use globals, you can use nested functions which can see parent's workspace.

MATLAB: Error using exp Too many input arguments.

The exp function doesn’t like the comma (,) as a decimal separator. Change it to a (.).

With that modification, this works:

tspan = [0 1500];
y0 = 0;
[t,y] = ode45(@(t,y) exp(-0.0001/8.314./(300+4000.*y./(421.8-7.8.*y))), tspan, y0);
plot(t,y)

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Related Solutions

MATLAB: Variable coefficients-help needed please!!!

MATLAB: Error using exp Too many input arguments.

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