# 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
clc

% 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.');
break;
end

b = a - fa/ga;
fprintf('step=%d\ta=%f\tf(a)=%f\n',step,a,fa);
a = b;

if step>N
disp('Not convergent');
break;
end
step = step + 1;
end

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
```