Engineering Homework Help

%The Newton Raphson Method

clc;

close all;

clear all;

syms x;

f=x*exp(x)-1; %Enter the Function here.

g=diff(f); %The Derivative of the Function

n=input(‘Enter the number of decimal place:’);

epsilon = 5*10^-(n+1)

x0= input(‘Enter the intial approximation:’);

for i=1:100

f0=vpa(subs(f,x,x0)); %Calculating the value of function at x0

f0_der=vpa(subs(g,x,x0)); %Calculating the value of function derivative at x0

y=x0-f0/f0_der; %The Formula

err=abs(y-x0);

if err<epsilon %checking the amount of error at each iteration

break

end

x0=y;

end

y=y-rem(y,10^-n); %Displaying upto required decimal places

fprintf(‘The Root is %fn’,y);

fprintf(‘No. of lterations: %dn’,i);