How to output derivative from ODE 45
52 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
I have the following function:
function dy = fluboard(t, pop, b, d, N)
dpop(1) = -b*pop(1)*pop(2)/N;
dpop(2) = b*pop(1)*pop(2)/N - d*pop(2);
dpop(3) = d*pop(2);
dy = [dpop(1); dpop(2); dpop(3)];
And call it by:
h=0.01; tspan=[0 20]; pop0=[760 3 0]; b=1.66; d=1/2.2; N=763;
[t y] = ode45(@fluboard, tspan, pop0, h, b, d, N);
How can I get the derivatives at each time point? Thanks.
0 Kommentare
Antworten (2)
Reen
am 7 Sep. 2017
If you want other varialbes along with the derivative, you can modify the function you call using ode45 to:
function [dy other_variable]= fluboard(t, pop, b, d, N)
If you just want the derivative you can keep it the same. Now you can run through the code you get your y vector. After that, run through a for loop calling the fluboard function to get your desired output. It should look something like this:
for i=1:length(y)
[dy(i) other_variable(i)] = fluboard(t(i), pop(:,i), b, d, N); % may have to use pop(i,:) instead depending on how the matrix is set up
end
That will just run through your function to find the derivative at each point.
3 Kommentare
Walter Roberson
am 7 Sep. 2017
The ode routines do not evaluate the function at each time point: they evaluate at nearby time points and predict the value at the specific time points. Any given output might or might not have been evaluated exactly.
James Tursa
am 7 Sep. 2017
@stuckedMD: If y is linear, then you would get y(t) = y(t-1) + dy(t-1). But y is not linear, so this relationship does not hold. That's the whole reason for calling the ode routines in the first place, because you are trying to solve problems where the solution is not simple and linear.
Star Strider
am 7 Sep. 2017
Bearbeitet: Star Strider
am 7 Sep. 2017
Taking the numerical derivatives using the gradient function is the easiest solution. For best results, this requires that tspan be a vector with a constant sampling interval, so I added that.
My approach:
fluboard =@(t, pop, b, d, N) [-b*pop(1)*pop(2)/N; b*pop(1)*pop(2)/N - d*pop(2); d*pop(2)];
h=0.01; tspan=[0 20]; pop0=[760 3 0]; b=1.66; d=1/2.2; N=763;
tspan = linspace(0,20);
[t y] = ode45(@(t,pop)fluboard(t, pop, b, d, N), tspan, pop0);
[~,dy] = gradient(y, mean(diff(tspan)));
figure(1)
subplot(2,1,1)
plot(t, y)
title('Solution')
grid
subplot(2,1,2)
plot(t, dy)
title('Derivatives')
grid
2 Kommentare
Star Strider
am 7 Sep. 2017
My pleasure
The gradient function calculates the central difference numerical derivative, except at the edges or ends, where it calculates a one-sided derivative. See the documentation on gradient for a full description.
You did not describe the error, so I cannot describe a way to prevent it. My code as I posted in my Answer ran without error.
Siehe auch
Kategorien
Mehr zu Graphics Performance finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!