Newton Raphson Method MATLAB Program with Output

This program implements Newton Raphson Method for finding real root of nonlinear equation in MATLAB.

In this MATLAB program, y is nonlinear function, a is initial guess, N is maximum number of permitted itertaion steps and e is tolerable error.

MATLAB Source Code: Newton-Raphson Method

% Clearing Screen

% Setting x as symbolic variable
syms x;

% Input Section
y = input('Enter non-linear equations: ');
a = input('Enter initial guess: ');
e = input('Tolerable error: ');
N = input('Enter maximum number of steps: ');
% Initializing step counter
step = 1;

% Finding derivate of given function
g = diff(y,x);

% Finding Functional Value
fa = eval(subs(y,x,a));

while abs(fa)> e
    fa = eval(subs(y,x,a));
    ga = eval(subs(g,x,a));
    if ga == 0
        disp('Division by zero.');
    b = a - fa/ga;
    a = b;
    if step>N
       disp('Not convergent'); 
    step = step + 1;

fprintf('Root is %f\n', a);

Bisection Method MATLAB Output

Enter non-linear equations: cos(x)-x*exp(x)
Enter initial guess: 1
Tolerable error: 0.00001
Enter maximum number of steps: 20
step=1	a=1.000000	f(a)=-2.177980
step=2	a=0.653079	f(a)=-0.460642
step=3	a=0.531343	f(a)=-0.041803
step=4	a=0.517910	f(a)=-0.000464
step=5	a=0.517757	f(a)=-0.000000
Root is 0.517757