ode45 is returning the incorrect solution

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!

Answer 1

[Ameer Hamza]

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.

[Koren Murphy]

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]

or the simplfied answer of (u*t + C), if integration limits are not specified

[Ameer Hamza]

I am not sure about your comment. Can you show the mathematical form of the differential equations?

[Koren Murphy]

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]

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]

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]

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.