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Simple Euler Method

##Usage:Call Octave from terminal
##and then call EulerMethodUmitAlkus.m
##from octave and finally
##press enter. That's all.
##Simple Euler Method
##Constants and initializations
x=[]; ## initial empty vector for x
y=[]; ## initial empty vector for y
x(1)=1; ## initial value of x
y(1)=1; ## initial value of y
h=1E-3; ## increment in x
dery=[]; ## 1st derivative of y wrt x
n=1; ## inital loop index for while
## enter the while loop for the interval x=[1,2]
while (x(n)<=2)
x(n+1)=x(n)+h;
dery(n+1)=x(n)*x(n)-2*y(n)/x(n); ##given
y(n+1)=y(n)+h*dery(n); ##Euler method
n++;
endwhile
##exit from the 1st while loop
##Modified Euler Method
##Constant and initializations
ymid=[]; ## empty vector function evaluated at x midpoint
xmid=[]; ## empty vector func. of midpoints in x
ymid(1)=1; ## inital value for ymid.
derymid=[]; ## derivative of y at midpoints
##Enter the 2nd while loop
n=1;
while (x(n)<=2)
xmid(n)=x(n)+h/2;
derymid(n)=xmid(n)*xmid(n)-2*ymid(n)/xmid(n);
ymid(n+1)=ymid(n)+derymid(n)*h/2;
n++;
endwhile
## Plot for Simple Euler Method
subplot(2,1,1)
hold on
plot(x,y,'r-');
title('Simple Euler Method');
xlabel('x');
plot(x,dery,'b-');
legend('y','dy/dx')
hold off
##Plot for Modified Euler Method
subplot(2,1,2)
plot(x,ymid,'g-');
title('Modified Euler Method');
xlabel('x');
ylabel('y-modified');
print('-dpsc','EulerMethodUmitAlkus.ps')
save -text EulerMethodUmitAlkus.dat

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