How to store a intermediate variable from ode45 function to the Workspace as a vector

Having a system of two odes

I put the odes in a function and the script to solve the given function

I would like to store ALL "n" values in the Workspace. If I use "global n", I can see just one value of the n (the last one). Could you please help me to find a way for that case?

Thanks in advance

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function dx=funx1x2(t,x)

global n

S=250;

CC=2.35;

DD=0.65;

%State variables

k=x(1);

q=x(2);

L=k*S*CC;

D=q*S*DD;

n=sqrt(L^2+D^2)

%Equations of motion

dx=zeros(2,1);

dx(1)=q;

dx(2)=0.5*t*k;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Solver

clc; clear all;

global n

[t x]= ode45(@funx1x2,[0 5],[0 0.5]);

Answer 1

[Jan]

Remember that the ODE45 integrator has a stepsize controller, which can reject steps, if they are outside the error tolerance. Therefore storing the local positions inside the function to be integrated can reply invalid results. In addition the function to be integrated is called multiple times per step, such that you'd get more values of n than you get for the trajectory x. Afterwards it is not trivial to find out, which n belongs to which x.

Obtaining the values is much easier than with evil global variables which are known to cause more troubles than they solve:

function Main
  % clc; clear all;  % No, do not clear all
  [t, x]  = ode45(@funx1x2, [0 5], [0 0.5]);
  [dx, n] = funx1x2(t, x.');
  figure;
  subplot(1,2,1);
  plot(t, x);
  subplot(1,2,2);
  plot(t, n, 'c');
end

function [dx, n] = funx1x2(t, x)
  S  = 250;
  CC = 2.35;
  DD = 0.65;
  k  = x(1, :);
  q  = x(2, :);
  L  = k * S * CC;
  D  = q * S * DD;
  n  = sqrt(L .^ 2 + D .^ 2);
  dx = [q; 0.5 * t * k];
end

Now funx1x2 is "vectorized": I accepts the input x as vector. Then the integrator calculates the trajectory at first and n is created for the evaluated time points afterwards. The 2nd output n is inored during the integration.

Another option would be to use the outputfcn, which is called for the accepted steps only, but this is more complicated.

[Jan]

[MOVED from section for answers:] Halil wrote:

First of all thank you so much for your help and detailed explanation. I applied the code which you explained above and now n is created as vector.

[Jan]

[MOVED from flags] Flagged by Changran He about 8 hours ago. ode save

@Cangran He: Please use flags only to inform admins an editors about inappropriate contents like spam or rudeness. Thanks.