DECOMPOSITION OF DIBORANE (B2H6) AND ADSORPTION OF BH3 ON GE(100)

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

TOPICS IN QUANTUM INFORMATION THEORY EXAM SOLUTIONS

Thank you Assoc. Prof. Dr. Sadi Turgut

NEWTON-RAPSON METHOD-8th degree Legendre polynomial

## Newton-Rapson Method to the smallest non negative root ## of the 8th degree Legendre Polynomial ## P8(x)=(1/128)(6435x^8-12012x^6+6930x^4-1260x^2+35) ## where -1<=x<=1. ## for the smallest non negative root, we can ignore ## all the terms except the last two by truncated ## the function to be zero and find ## x=0.167 as the initial smallest non negative ## root. ##Constants and initializations x=[]; ## Empty array for the iterated x roots x(1)=0.16700000; ## Initial guess to begin the iteration for the ## smallest non-negative root. L8=[]; ## Empty array for the Legendre polynomial L8p=[]; ## Empty array for the derivative of the Legendre polynomial for i=1:100 ##The value of the function at x L8(i)=(1/128)*(6435*x(i)^8-12012*x(i)^6+6930*x(i)^4-1260*x(i)^2+35); ##The value of the derivative of the function at x L8p(i)=(1/128)*(6435*8*x(i)^7-12012*6*x(i)^5+6930*4*x(i)^3-1260*2*x(i)); x(i+1)=x(i)-L8(i)/L8p(i); ## the iteration endfor ## For plot let's

Ümit Alkuş

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