# How to solve coupled differential equation of expansion coefficients numerically?

I want to solve the following set of coupled differential equations for $C_{n}$s numerically:

$\frac{dC_{n}(t)}{dt}=\sum_{m=0}^{\infty}f_{m,n}(t)C_{m}(t)$

How should I code this in Mathematica?

• Should f(t) be f_m(t), or can it be taken outside the sum? I think you need to provide some more information about the assumed behaviour and boundary conditions of your functions. May 10 '17 at 20:41
• @mikado I corrected the post. I don't need to know how to solve it right now. I want to know that how can I code it. I know how to use NDSolve for usual differential equations. But What about this type? May 10 '17 at 20:53
• @bbgodfrey Let's assume that $n=1,2$ and $m=1,2$. How can I transform it to canonical form? Can you provide a minimal code? May 11 '17 at 7:12
• My earlier comment was wrong. Sorry. However, for a finite number of equations, NDSolve[Thread[D[c, t] == c.f, bc], c, {t, tmin, tmax}] should work provided equations are not singular or stiff. Here, c is vector of dependent variables,f is matrix of coefficients, and bc is vector of initial conditions. An infinite number of equations cannot be solved numerically in finite time except under unusual circumstances. May 11 '17 at 13:21