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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
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.

Fangjun Jiang
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);

Naz
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

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