ode 45 giving the wrong solution

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tomer polsky
tomer polsky on 15 Feb 2018
Commented: James Tursa on 15 Feb 2018
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 ?
  3 Comments
Jan
Jan on 15 Feb 2018
"oilers method"?! The famous mathematician was called Euler, Leonhard Euler.
James Tursa
James Tursa on 15 Feb 2018
Maybe Wayne Gretzky is involved with this somehow ...

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Answers (1)

Jan
Jan on 15 Feb 2018
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

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