How to solve vectorial differential equation with ode45

I have a system of differential equations in the time domain which have been discretized in the room domain, so the original equations looks something like

g''+C*g = A*g+f(t)

where g'' is the time-derivative, A is a matrix (NxN), and f a vector, and thus g and g'' is also a vector (both Nx1)

The problem arises when I try to solve the system (which I've rewritten to a system of first order equations) with ode45,

[t,y] = ode45(@(t,y) ODE(t,y,A,k),t_span,v0);

where it returns a dimension mismatch due to A*g in the ODE, which should be fine, but ode45 makes g a scalar and not a vector.

Any thoughts on how I should proceed?

Code:

global rho x dx N
N = 10;
L = 1;
dx = L/(1+N);
A = zeros(N,N);
x = zeros(N,1);
%Normalised constants and matrix initialisation
%....

t_span = [0 ceil(100*k)];
v0 = zeros(N,2);

[t,y] = ode45(@(t,y) ODE(t,y,A,k),t_span,v0);

ODE:

function dvdt = ODE( t,v,A,k )
dvdt = zeros(2,1);
dvdt(1) = v(2);
dvdt(2) = A*v(1)+f_func(t)-2*v(2);
end

f_func:

function [ f_func ] = f_func( t )
%returns vector of size Nx1
end

[Torsten]

We'll have to see the complete code to help.

Best wishes

Torsten.

[anmo]

I've added the code-snippets

[Jan]

Using the same name for the output and the function is confusing: "function [f_func] = f_func(t)"

Answer 1

[Torsten]

In ODE, v must be a vector of length (2*N) (not a matrix of size (N,2)).

The first N components could contain x0, the last N components v0.

Same for dvdt: it must be a column vector of length (2*N).

The first N components could contain velocity, the last N components could contain acceleration.

Best wishes

Torsten.

[anmo]

That did it! Thank you!

Answer 2

[Jan]

dvdt(2) = A*v(1)+f_func(t)-2*k*v(2);

Here A is a matrix and the reply of f_func(t) is a vector. The result must be a scalar.

The dimensions of the variables in this line do not match. I cannot guess the intention, because all I see is the failing code. Therefore I cannot suggest an improvement.