how do I pre-allocate the program. It highlights it in red and I am not able to do that. Thanks for helping.

for i=1:numel(rho)-1
rho0=17.1;

zspan = [z(i) z(i+1)];
NS =(rho(i+1)-rho(i))/(z(i+1)-z(i));
[t,v] = ode45(@(t,v)rhs(t,v,NS), zspan, v0);
v0 = [v(end,1) ; v(end,2) ; v(end,3)];
zsol =  [zsol;t];
v1sol = [v1sol;v(:,1)];
v2sol = [v2sol;v(:,2)];
v3sol = [v3sol;v(:,3)];
end

[Greg]

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Answer 1

[Guillaume]

Assuming your ODE returns a 3x3 array:

v1sol = zeros(3, numel(rho) - 1);
v2sol = zeros(3, numel(rho) - 1);
v3sol = zeros(3, numel(rho) - 1);
zsol = zeros(numel(rho) - 1, 1);
rho0=17.1;
for i=1:numel(rho)-1
   zspan = [z(i) z(i+1)];
   NS =(rho(i+1)-rho(i))/(z(i+1)-z(i));
   [t,v] = ode45(@(t,v)rhs(t,v,NS), zspan, v0);
   v0 = [v(end,1) ; v(end,2) ; v(end,3)]; 
   zsol(i) = t;
   v1sol(:, i) = v(:, 1);
   v2sol(:, i) = v(:, 2);
   v3sol(:, i) = v(:, 3);
end

[Greg]

I would go ahead and use

nrho = numel(rho) - 1;

Just a little cleaner in my opinion. Nothing to do with pre-allocation.

Answer 2

[Dereje]

@Guillame there is an error(Matrix mis-match) on

 sol(i) = t;

@Greg I don't understand your point.

[Greg]

Please use the "Comment on this Question" and "Comment on this Answer" links instead of creating a new answer. I know the web form is confusing the first time.

You can also edit your original question to attach the code. This makes it easier for others (people may have the same question you have) to find.

Answer 3

[Dereje]

I have attached my original codes.