Same time steps for ODE function and OutputFcn

In the following model, I need to know the values of the model parameter 'k' along with 'y'. To find k, I used 'OutputFcn'. However, after runing the model, I get different lengths for the k array (13) and 'y' array (94). But what I need to know is the value of k each iteration uses to compute each 'y' value (or simply, similar lengths for both arrays). In addition, I see that 'x' (equivalent to time) called in the ODE function also has a different array length (94) compared to that of the same 'x' called in OutputFcn (13). I get that the reason behind this is the fact that OutputFcn generates parameter values after each integration timestep rather than after every call of the ODE function. I thought I will perhaps solve the issue by asssigning fixed time steps to the ODE function. But the issue remains the same. Is there anyway I can modify the script where both OutputFcn and ODE function would return the same array lengths for 'k' and 'y' using same 'x'? Or else is there any other method I can get my expected result? Any help is much appreciated.

Thank you!

global k_all kx
options = odeset('Reltol', 1e-3, 'OutputFcn', @get_process, 'MaxStep', 100, 'InitialStep', 1);

kx = []; % both l and x values together
k_all = []; % All values

t0 = 0;
tf = 2000;
tspan = t0:0.005:tf;
[x,y] = ode45(@myode,tspan,1,options);


function dydx = myode(x, y)

global kx
k = x.^2 + y.^2;
kx = [k x];
dydx = x + k.*y;
end


function [status] = get_process(x, y, flag);

global kx k_all

k_all = [k_all; kx];
status = 0;
end

Answer 1

[Alan Stevens]

You could simply calculate

k = x.^2 + y.^2;

immediately after

[x,y] = ode45(@myode,tspan,1,options);

However, have you really looked at your ode? You have, in effect,

dy/dx = x + x.^2.*y + y.^3;

and you start from y = 1.

y blows up extremely rapidly and the ode solvers won't converge after x is slightly greater than 0.4, so there's no way you are going to get to x = 2000.