##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(...
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