Question

This is Matlab Problem and I'll attach problem1 and its answer for reference.

Answer 1

MATLAB Script:

close all
clear
clc

syms x
f = x*exp(x) - 5;
[r, x_save] = newton(f,3,[],10)
fid = fopen('A2.dat', 'w');
for i = 1:length(x_save)
fprintf(fid, '%f\n', x_save(i));
end
fclose(fid);

function [r, x_save] = newton(f,x0,tol,N)
if nargin < 3 || isempty(tol), tol = 1e-4; end
fp = matlabFunction(diff(f));
f = matlabFunction(f);
x = zeros(1, N+1);
x(1) = x0;
x_save = x(1);
for n = 1:N
if fp(x(n)) == 0
r = 'failure';
end
x(n+1) = x(n) - f(x(n))/fp(x(n));
x_save = [x_save x(n+1)];
if abs(x(n+1) - x(n)) < tol
r = x(n+1);
break
end
end
x_save = x_save(:);
end

Output:

r =
1.3267
x_save =
3.0000
2.3122
1.7637
1.4356
1.3347
1.3268
1.3267

Contents of the file 'A2.dat':

A2.dat 3.000000 2.312234 1.763651 4 1.435621 5 1.334709 1.326770 7 1.326725