output extra variables through ode23 when there are multiple unknowns

By writing a function below, one can output extra variable v (other than unknown u):

function [ut,v]=myode(t,u)
ut=u;v=u+1;

Then output v below (V):
[T,U]=ode23(@myode,[],...)
[Ut,V]=myode(T,U)

But perhaps the above approach only works for the case where the ODE in question has only 1 unknown. When there're multiple unknowns, U will be a matrix rather than a vector. Then how to execute the last sentence above when U as an argument isn't a column vector?

[Ameer Hamza]

You can solve multi-variable differential equations using ode23 by outputting them as elements of a vector. What do your differential equations look like?

[feynman feynman]

Yes, normal solution of multi-variable differential equations can be done via ode23. The ODEs can look anything, quite long. But my issue is with outputting internal variables during the ode solution process.

Answer 1

[Walter Roberson]

Use persistent variables in myode to record all v values ever generated internally. Then have myode check nargout > 1 and if so then assign that record to the second output variable. ode23 will not normally request two outputs, so you can use the request for two outputs (from your manual call to myode) to return the record.

However... It will not work in practice. The ode*() routines do not output one row for each call to myode(): they make a few calls to adjust error estimates, and synthesize a projected output within the required error tolerance. In general the ode*() routines can even go backwards in time to make adjustments (but not all of them do go backwards in time.)

Returning a record of internal variables is only robust if you record all of the relevant information and dump it all, understanding that it will not correspond exactly to the values returned by the original ode*() call.

Answer 2

[Ameer Hamza]

As Walter mentioned, it is not possible to record have multiple output values when using ode23; neither does declaring variables as persistent or global will because of extra calls to myode. But you can tweak your system of differential equations to output any other variable you want. For example, consider the following differential equation

.

Suppose, you also want to output some other values, like and , so you can write the following equivalent system of differential equations

, derivative of

, derivative of

Then you can write myode as

function dydt = myode(t,y)
    dydt(1) = y(1);
    dydt(2) = 2*t;
    dydt(3) = 3*t.^2 + dydt(1);
    dydt = dydt(:);
end

and call the ode45 as

[t,y] = ode45(@myode, [0, 5], [1, 3, 1]);

The ode45 will output the value of all the three variables.

[feynman feynman]

@ameer thanks a lot, this surely will do but it might increase unnecessary workload when the ODE to solve contain a huge number of unknowns, say the unknown u vector has 100 components.

[feynman feynman]

@ameer thanks a lot, this surely will do but it might increase unnecessary workload when the ODE to solve contains a huge number of unknowns, say the unknown u vector has 100 components.

[Ameer Hamza]

Yes, that true. I will cause overhead as compared to just calculating the values later.