I'm not sure how the following works with matlab. Imagine I have a set of coupled ODEs defined by the following (n x 1) vector:
beta' = K0 beta + beta' H0 beta
where K0 is a (n x 1) and H0 is (n x n). Some of the elements of beta can be solved in closed form and so I have explicit solutions while the rest need to be solved numerically. I'm unsure where to begin in terms of using ODE45 or the like in terms of coding these equations. For example, is it possible to write a function inside one of the elements of beta? For example, if I know the solution to beta_3 ?
Obviously I could just multiple this out line by line but this is somewhat inefficient and prone to mistakes. I guess my question really relates to vectorizing ODE systems. Any pointers would be greatly appreciated.