ode45 is returning the incorrect solution

2020 3 17
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更新时间：2020 3 17
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I am running an ode45 to solve a simple intergration. The intergration is so simple I can perform it by hand - hence knowing the solution returned is excessively large.
function [Output] = ContinuousFeed(t,u)
uA = u(1);
uB = u(2);
uE = u(3);
uF = u(4);
u = [uA; uB; uE; uF];
Output = u;
end
t=[0 10];
u0 = [1; 0.0002; 0; 0];
[t, u] = ode45 (@ContinuousFeed, t ,u0);
Why is it returning a final value of 22030.53 for the first column? All other columns are displaying inaccurate answers also.
Thank you!

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Ameer Hamza
Ameer Hamza 2020-3-17
编辑：Ameer Hamza 2020-3-17

0 个投票

The MATLAB is giving the correct solution. You are solving four independent ODEs of the form
which have an anatylical solution
The solution of ode45 matches this analytical solution.

7 个评论
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Koren Murphy
Koren Murphy 2020-3-17
U is meant to be a constant however, so how should this be implemented to give a solution of;
int u = [u*tj - u*ti]?
Koren Murphy
Koren Murphy 2020-3-17
or the simplfied answer of (u*t + C), if integration limits are not specified
Ameer Hamza
Ameer Hamza 2020-3-17
I am not sure about your comment. Can you show the mathematical form of the differential equations?
Koren Murphy
Koren Murphy 2020-3-17
This is the equation i have to integrate. U is a constant feed rate, however, must be intregated to solve a larger problem. I have used ode45 to solve other aspects of the problem but as it it solving using a linear equation the solution is accurate.
I really appreciate your assistance.
Steven Lord
Steven Lord 2020-3-17
编辑：Steven Lord 2020-3-17
Be careful with your variables. I think you're overloading the variable u with two meanings.
Do you want to solve the system or the system ? If the latter your ODE function should be:
function dudt = ContinuousFeed(t, u)
yourConstantVector = [1; 2; 3; 4]; % For example
dudt = yourConstantVector;
end
Note that nothing in this version of ContinuousFeed depends on the time t or the function u at all so you could replace them with ~ (to tell MATLAB explicitly that ContinuousFeed doesn't use thoe inputs.)
function dudt = ContinuousFeed(~, ~)
yourConstantVector = [1; 2; 3; 4]; % For example
dudt = yourConstantVector;
end
Koren Murphy
Koren Murphy 2020-3-17
I have applied this Steven and it has stopped the exponential. However, it appears to be adding the original feed to the solutions as it goes
function dudt = ContinuousFeed(~, ~);
ConstantVector = [1; 0.0002; 0; 0]; % initial conditions
dudt = ConstantVector;
end
r = 1e-6;
t = [0 10 10+r 20 20+r 30 30+r 40 40+r 50]; % this is assuming a sample taken every 10 units of time.
% tspan must constantly
% increase or decreases to
% work hence the addition of 1e-6
u0 = [1; 0.0002; 0; 0];
Therefore it is returning the solutions;
1
11
11.000001
21
21.000001
31
31.000001
41.
41.000001
51.
Ameer Hamza
Ameer Hamza 2020-3-17
If my initial feed you meant initial conditions, then this is the expected behavior. Vector u0 tells the ode45 where to start the solution of each variable.

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