ode 45 giving the wrong solution

hello i am trying to use ode command to solve this eqution using ode command :

function [ x_diff_ode ] = x_ode_method( t,x )

global A_a A_b B_a B_b f U t_on C_a C_b

     ratio=rem(t,(1/f));

     S_switch_a=ratio<t_on;

     A_total=A_a*(S_switch_a)+A_b* not(S_switch_a);
     B_total=B_a*(S_switch_a)+B_b*not(S_switch_a);

x_diff_ode= A_total*x+ B_total*U;

end

how ever this is giving me the wrong plot , and when i did it numericly using oilers method i got the the right plot ,here is the code using oile'rs method :

function [x_zigzag,t,z,V_R_oilers_theory,switch_a,t_switch] = eulers_method_numeric_sulution( A_a,A_b,B_a,B_b,f,U,t_on,C_a,C_b,number_of_points, number_of_cycles )

T=1/f;

%  number_of_cycles=900;

%  samples_per_cycle=300;

   total_samples=number_of_points;
   run_time=(T)*(number_of_cycles);

x1_zigzag=[0;0;0;0];

t=linspace(0,run_time, total_samples+1);

% t_delta=(T)/(samples_per_cycle);

t_delta=(run_time-0)/(total_samples+1);

for i=1:total_samples

      ratio(i)=rem(t(i),(T));
      S_switch_a(i)=ratio(i)>t_on;

       A_total=A_a* S_switch_a(i)+A_b* not(S_switch_a(i));
       B_total=B_a* S_switch_a(i)+B_b*not(S_switch_a(i));
       C_total=C_a* S_switch_a(i)+C_b*not(S_switch_a(i));

       x1_zigzag(:,i+1)=x1_zigzag(:,i)+t_delta*( A_total*x1_zigzag(:,i)+B_total*U);

        V_R_oilers_theory(:,i+1)=C_total*x1_zigzag(:,i+1);

end

x_zigzag= x1_zigzag;
t=t;
z=t_delta;
V_R_oilers_theory=V_R_oilers_theory;

switch_a=S_switch_a;
t_switch=total_samples;

end

my question is why the ode command fails and giving me the wrong plot ? and how can i fix it ?

[Walter Roberson]

Any time I see a global variable in an ode function I assume that it is empty or has an unexpected value. I do not bother to try debugging anything else about the ode function until the global variables have been eliminated.

https://www.mathworks.com/help/matlab/math/parameterizing-functions.html

[Jan]

"oilers method"?! The famous mathematician was called Euler, Leonhard Euler.

[James Tursa]

Maybe Wayne Gretzky is involved with this somehow ...

Answer 1

[Jan]

 why the ode command fails and giving me the wrong plot

You did not show us your "ode command".

Your function to be integrated contains a discontinuity:

S_switch_a = ratio < t_on;

This is a DON'T for the numerical integration, because standard integrators as Matlab ODE45 are designed to handle smooth functions only. See http://www.mathworks.com/matlabcentral/answers/59582#answer_72047