Dimension mismatch in defining a function for use in ode45

Hi,

I'm solving a system of ODEs with ode45. I would like to have extra (non integrated) parameters out of the function as in here

http://www.mathworks.co.uk/support/solutions/en/data/1-196SD/?solution=1-196SD

However for my problem I need to pass in more information too. If I have:

function [dydx k] = myodesimple(x, y, flag, c)
k = x.^2 + y.^2;
dydx = x + k.*y + c;

I can solve using [x,y]=ode45('myodesimple',[0 0.5 1],[0.3]). Then I can use [dydx k]=myodesimple(x,y) to recover k for any x time steps and y solutions.

If I change the function to take in another scalar parameter, say c. I can still recover k after solving with using [x,y]=ode45('myodesimple',[0 0.5 1],[0.3],flag,0.08) by using [dydx k]=myodesimple(x,y,flag,c). The problem comes when trying to solve two equations in the function. If I introduce another eqn:

    function [dydx k] = myodecomplex(x, y, flag, c)
    k(1) = x.^2 + y(1).^2;
    dydx(1) = x + k.*y(1) + c;
    dydx(2) = x + (4.*c).*y(2);
    k=k(1)’;
    dydx=dydx';

Then ode45 will run with [x1,y1]=ode45('myodecomplex',[0 0.5 1],[0.3 0.2],[],0.08), so I can obtain solutions. However I can no longer obtain k (which should be a column vector). There seems to be something wrong with the dimensions of the vectors I am using but I cannot work out where! The error I get when trying [dydx k]=myodecomplex(x1,y1,flag,0.08) is

"??? In an assignment A(I) = B, the number of elements in B and I must be the same.
Error in ==> myodecomplex at 2
 k(1) = x.^2 + y(1).^2;

Any ideas on how I can obtain k, having gained solutions?

Answer 1

[Jan]

In your code x is a vector, such that:

x.^2 + y(1).^2;

is a vector also. Therefore it cannot be assigned to the scalar k(1). The expression k(1)' is meaningless, because k(1) is a scalar, which is not affected by a transposition. I guess, that you want k instead of k(1).

To pass parameters to the function, use anonymous functions as explained here: Answers: benefit of anonymous functions when using ODE45.