Lecture 4: Newton s Method Matlab

Newton’s Method

Write the program in the editor page by clicking on New Script , Save it , then click Run.

Example; Find an approximation root to the following equation with error ? =0.0001, and initial point x0 =3:
f(x)=x^2-4 sin?x

Solution:
f=inline( x^2-4*sin(x) );
d=inline( 2*x-4*cos(x) );
x0=input( x0= );
n=input( n= );
disp( x0 x1 )
for i=1:n
if d(x0)==0
disp( division by zero, can not proceed. )
break
end
x1=x0-f(x0)/d(x0);
disp([x0 x1])
if abs(x1-x0)<=0.0001
break
else
x0=x1;
end
end

Solution:
x0=3
n=9

x0 x1
3.0000 2.1531
2.1531 1.9540
1.9540 1.9340
1.9340 1.9338
1.9338 1.9338

Exercises:
Q1\ Do exercises in your previous Lectures using Newton’s Method
Q2\ Use all three methods in this Section to find solutions to within 10?5 for the following problems.
a. 3xex = 0 for 1 ? x ? 2
b. 2x + 3 cos x ? ex = 0 for 0 ? x ? 1