Calculating and Adding Percent Error to a Graph

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]

Apply {}Code format next time.

[Karen]

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

Answer 1

[Fangjun Jiang]

Since you have the y and ystar, you can do

percent_error=100*abs(y-ystar)./y;

Notice "./" is the element-wise division.

[David Young]

Yes, though also y needs to be a vector, so needs y(i+1) = ... inside the for-loop.

[Karen]

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]

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]

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

Answer 2

[Naz]

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]

Thank you.