Solution to Nonlinear Differential Equation

I want to solve the Equation numerically

but I don't know how to write the code.

D is a square Matrix with constant values.

[Alan Stevens]

If D has constant values you have a set of simultaneous linear differential equations. Do you have a set of conditions for the fi?

[christoph weihs]

I have the conditions that f and f' have to be 0 for i=0 and f' is ->1 for i->n

[Walter Roberson]

Is that a Mass Matrix?

https://www.mathworks.com/help/symbolic/solve-daes-using-mass-matrix-solvers.html

Answer 1

[Alan Stevens]

Here is some example code using arbitrary data:

f0 = [0; 1; 2];   % initial conditions
tspan = [0 2];    % integration limits

[t, f] = ode45(@rates,tspan,f0);    % ode solver

plot(t,f)  % plot results

% function that calculates rates of change of f 
function dfdt = rates(~,f)

        D = [1 2 3; 0.4 0.2 -0.1; 1.6 1.7 -1.8];
        dfdt = D*f;

end

Is this the sort of thing you are looking for (obviously you would need to enter your own data).