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FIBER OPTIC EXPERIMENT I

Thank you Assoc. Prof. Dr. Hakan Altan

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SIMPLE AND MODIFIED 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 dery(1)=0;## 1st entry of dery 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+1); ##Euler method n++; endwhile ##exit from the 1st while loop ##Modified Euler Method ##Constant and initializations x(1)=1; ## beginnig of the interval [1,2] ymod(1)=1; ## inital value for modified y. ymid=[]; ## empty vector function evaluated at x midpoint xmid=[]; ## empty vector func. of midpoints of the interval h in x-axis. derymod=[]; ## modified derivatives of ymod

TOTAL DISPLACEMENT OF LOOPLESS RANDOM WALK

## A for good and evil as well as loopless ## total displacement function of random walk ## that takes in the step numbers as an ## argument and returns the displacement ## of the rnd walker.Note that the probabilities ## to turn rigth and left are equal but the left ## step is twice the rigth step. ## Usage : rw_uneven(N) function rw_uneven(N) rn=rand(N,1); ## If the element of a random vector r=-(rn<0.5); ## is smaller than 0.5, then return -1, li=find(r == 0); ## Else return 2(equal probability). r(li)=2; x=sum(r) ## total displacement endfunction