Calculating and Adding Percent Error to a Graph

Karen (view profile)

on 23 Nov 2011
Accepted Answer by Fangjun Jiang

Fangjun Jiang (view profile)

The Percent Error = 100*abs(exact solution-Approximate solution)/Exact Solution. I am writing a Euler method approximation and I need to know how best to present this. I keep getting the error message that "matrix dimensions must agree". Here is my code.
%Script that demonstrates Euler integration for a first order problem using
%MATLAB.
%The problem to be solved is:
%y'(t)+2*y(t)=2-exp(-4*t)
%This problem has a known exact solution
%y(t)=1+0.58*exp(-4*t)-0.5*exp(-2*t)
function ystar = Eulermethod20(n)
a=0;
b=5;
h=(b-a)/n;
t=0:h:5;%Initialize time variable
clear ystar;%wipe out old variable
ystar(1)=1.0;%Initial condition (same for approximation)
for i=1:length(t)-1, %Set up "for" loop
k1=2-exp(-4*t(i))-2*ystar(i); %Calculate the derivative
ystar(i+1)=ystar(i)+h*k1;%Estimate new value of y
end
%Exact solution
y=1+0.5*exp(-4*t)-0.5*exp(-2*t);
%Plot approximate and exact solutions
plot(t,ystar,'b--',t,y,'r-');
legend('Approximate','Exact');
title('Euler Approximation');
xlabel('Time');
ylabel('y*(t), y(t)');
percent_error= 100*(1)+(0.5*exp(-4*t)-(0.5*exp(-2*t))-(2-exp(-4*t(i)))-(2*ystar(i))/((1)+(0.5*exp(-4*t))-(0.5*exp(-2*t))));
legend('Percent Error')
The program runs, but the percent error doesn't calculate correctly. I need to calculate and show the error for this project and I was hoping someone can help. Thanks!

Fangjun Jiang

Fangjun Jiang (view profile)

on 23 Nov 2011
Apply {}Code format next time.
Karen

Karen (view profile)

on 23 Nov 2011
I don't even know what {} code is. No formal matlab training.

Answer by Fangjun Jiang

Fangjun Jiang (view profile)

on 23 Nov 2011

Since you have the y and ystar, you can do
percent_error=100*abs(y-ystar)./y;
Notice "./" is the element-wise division.

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Karen

Karen (view profile)

on 23 Nov 2011
It was great not getting an error message from MATLAB when I ran the code! Thanks, and then how can this error calculation get displayed on the graph?
Here is the code that I'm failing at:
percent_error=100*abs(y-ystar)./y;
Error(percent_error); %Is something wrong at this line?
%Plot approximate and exact solutions
plot(t,ystar,'b--',t,y,'r-');
legend('Approximate','Exact','Error');
title('Euler Approximation');
xlabel('Time');
ylabel('y*(t), y(t)');
Fangjun Jiang

Fangjun Jiang (view profile)

on 23 Nov 2011
y is a vector because t is a vector.
error() is a function but is for a completely different purpose. I don't understand your usage of Error(). Is Error() a user-defined function? If it is, you'd better use a different name even it is using capital "E".
You can just plot the error with your y and ystar.
plot(t,ystar,'b--',t,y,'r-',t,percent_error,'g');
Or put it in a separate figure because it is in a small scale.
figure;plot(t,percent_error);
Karen

Karen (view profile)

on 23 Nov 2011
Thank you very much. I'll plot it on a different figure to be able to see it better.

Naz (view profile)

on 23 Nov 2011

You are missing the 'dot' in the following expression:
percent_error= 100*(1)+(0.5*exp(-4*t)-(0.5*exp(-2*t))-(2-exp(-4*t(i)))-(2*ystar(i))./((1)+(0.5*exp(-4*t))-(0.5*exp(-2*t))));
Now this should work

Karen

on 23 Nov 2011
Thank you.