MATLAB: Error when using ode45 command,”returns a vector of length 11, but the length of initial conditions vector is 1.”

errorfunctionMATLABode45vector

function dw_dt = equation_(t,w)
a = 1;
b = 1.35;
v= [.6:.01:.70].';
dw_dt = a*w.^(v)-b*w;
%actual script
time_period = [0 20];% time period between 0 and 20 weeks
w0 = 0.5;% intial weight of the fish 
[t,w] = ode45('equation_',time_period,w0);

I'm trying to run my function using ode45. I should be able to run the function for every value of yv but for some reason i can't. when ever i try to run the function for once value of V is works perfectly fine but when i try to run it for every value of v it does not work well.

Best Answer

Hello,

The way the ode45 command works (as I'm sure you know) is that given a state vector, in your case w, you provide a function that evaluates the derivative of w and returns dw.

A common example is with position and velocity:

state_vec = [position; velocity];

where as your 'equation_' would return:

dstate_vec = [velocity; acceleration];

it seems like you understand this; however, you are giving it an initial condition of .5, so:

w = .5;

then you are returning a dw that is a vector (because v is a vector and is apart of the computation).

So ode45 is trying to update a constant .5 with a vector dw, this is where you are encountering your error. You can fix this by either changing your dw to a scalar result, or making your initial condition an equally long vector corresponding to the length of the returned dw.

Hope this helps!

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MATLAB: How to solve differential equations of motion of second order, which are changing depending on if/else conditions

Do you know (before calling the ODE solver the first time) when the ODE function that you're trying to solve changes based on the condition? If so call ode45 to solve the first ODE function up until that point then use the final result from solving that first ODE function as the initial condition for a second ode45 call using the second ODE function.

As a slightly more concrete explanation, let's say you know that the ODE you need to solve changes every 2 seconds. Solve the first ODE with a time span of [0 2]. Use the solution of that first ODE to define the initial condition for the second ODE and solve that second ODE with a time span of [2 4]. Repeat that process, using the solution of the second ODE to generate the initial condition for the third ODE and so on.

If you don't know exactly when the ODE you're trying to solve will change based on the condition, use an Events function. There's an example that uses Events in MATLAB called ballode. It's not exactly the same as the situation you described, since the ODE doesn't change, but if you imagine passing different function handles into the ODE solver based on which condition/event is "active" you should be able to adapt it to suit your purposes.

MATLAB: ODE45 to solve vector ode

You have a six element state vector. The y(1) and y(2) coming into your derivative function are not position and velocity vectors, they are the x and y position elements. It would probably be easier to write a short function for the derivative because of the calculations involved:

function dy = gravity(y,mu)
R = y(1:3);
V = y(4:6);
Rmag = norm(R);
RDOT = V;
VDOT = -mu * R / Rmag^3;
dy = [RDOT;VDOT];
end

Then call ode45 with a function handle that passes y and mu to the gravity function:

[ts,ys] = ode45(@(t,y)gravity(y,mu),tspan,ic);

ode45 isn't well suited for the orbit problem. You may have to use odeset( ) to create some tight tolerances to pass in to ode45 to get good results.

Best Answer

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