# How to solve an ODE with ode45 in a parfor loop?

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e_frog on 29 Oct 2020
Commented: e_frog on 29 Oct 2020
I have the following code:
function [t,S] = solve_ode(fg_vars,tspan)
inital_conds = [0 0];
t = zeros(65,1);
S = zeros(65,2);
parfor i = 1:100
[t(:,i), S(:,i)] = ode45(@(t,s) fn(t,s,fg_vars),tspan,inital_conds)
end
t = t(:)
S = S(:)
end
Which gives me the following error:
Unable to perform assignment because the size of the left side is 65-by-1 and the size of the right side is 65-by-2.
I dont understand why this error occures, because when I try to calculate the ODE without the pafor loop, the produced solutions are of this size:
t = 65x1 double
S = 65x2 double
Thanks!

KSSV on 29 Oct 2020
Edited: KSSV on 29 Oct 2020
[t(:,i), S(:,i)] = ode45(@(t,s) fn(t,s,fg_vars),tspan,inital_conds)
In the above t will be a column vector and S will be a column matrix with two columns. You cannot save like that. You can do
T = cell(100,1) ;
S = cell(100,1) ;
for i = 1:100
[t, s] = ode45(@(t,s) fn(t,s,fg_vars),tspan,inital_conds) ;
T{i} = t ;
S{i} = s ;
end
The above cannot be used with parfor...you cannot index the parfor loop.
e_frog on 29 Oct 2020
I actually did have to switch a t with a T and it is running now. BUT: now matlab just does the same calculation 100 times, instead of splitting the one calculation for tspan up between the cpu cores. So now the calculation takes actually 100 times longer than without any loop at all. Thats not what i wanted. I NEED to use the parfor loop. How can I achieve that?