Change input at each time step of the ODE solver 'ode45'

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KC
KC 2015-12-5
评论： Jan 2017-5-5
I am not sure how to change an input parameter 'β' at each time step. My code is below - which gives me an error. Can anybody help please!
t = [7 14 21 28 35 42 49 56 63 70 77 84];
for i=1:12;
beta(i) = 0.43e-08 + (4.28e-08 - 0.43e-08)*exp(-0.20*t(i));
end
f = @(t,x) [3494-0.054*x(1)-beta*x(1)*x(3); beta*x(1)*x(3) - 0.41*x(2); ...
50000*x(2) - 23*x(3)];
[t,xa1] = ode45(f,t,[64700 0 0.0033],beta);
  1 个评论
Jan
Jan 2015-12-5
And the error message is:
Error using vertcat
Dimensions of matrices being concatenated are not consistent.
Error in @(t,x)[3494-0.054*x(1)-beta*x(1)*x(3);beta*x(1)*x(3)-0.41*x(2);50000*x(2)-23*x(3)]

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采纳的回答

Jan
Jan 2015-12-6
Please consider, that Matlab's ODE integrators cannot handle non-smooth functions sufficiently. See http://www.mathworks.com/matlabcentral/answers/59582#answer_72047 .
The only reliable method to run the integration is a loop over the time intervals:
function yourIntegration
tResult = [];
xResult = [];
tStep = [7 14 21 28 35 42 49 56 63 70 77 84];
x0 = [64700 0 0.0033];
for index = 2:numel(tStep)
% Integrate:
beta = 0.43e-08 + (4.28e-08 - 0.43e-08) * exp(-0.20*t(index - 1))
af = @(t,x) f(t, x, beta);
t = tStep(index-1:index);
[t, x] = ode45(af, t, x0);
% Collect the results:
tResult = cat(1, tResult, t);
xResult = cat(1, xResult, x);
% Final value of x is initial value for next step:
x0 = x(end, :);
end
function dx = f(t,x, beta)
dx = [3494-0.054*x(1)-beta*x(1)*x(3); ...
beta*x(1)*x(3) - 0.41*x(2); ...
50000*x(2) - 23*x(3)];
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Saiprasad Gore
Saiprasad Gore 2017-5-5
Thanks a lot, I had a similar problem. I wanted to switch the eqn depending on condition after every step. I hope this will work in my case too. Can you tell me how to give ode45 just 1 step without intermediate adaptive steps?

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更多回答（1 个）

Walter Roberson
Walter Roberson 2015-12-6
f = @(T,x) [3494-0.054*x(1)-interp1(t,beta,T,'linear','extrap')*x(1)*x(3); interp1(t,beta,T,'linear','extrap')*x(1)*x(3) - 0.41*x(2); ...
50000*x(2) - 23*x(3)];
  2 个评论
sam
sam 2016-6-15
编辑：sam 2016-6-16
@Walter Roberson
Hi Walter,
Why do we have to do interpolation if we already know the exact expression of the variables? Couldnt we just input the exact expression of the variables into the Matlab ode45 solver? If we could, could you kindly tell me how to do this? Thanks.

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