Umm Al-Qura University
College of Engineering and Islamic Architecture
Electrical Engineering Department
Computational Method
LECTURE DATE:
SUBMISSION DATE:
LABWORK # 9:
Newtons Method
Prepared by
STUDNTE NAME 431xxxx
GROUP #
INSTRUCTOR: ENG. Muhammad Masud
SIGN:
Q. The nonlinear system:
have the approximate solution (0.5, 0,−0.52359877)t. Apply Newton’s method to this
problem with x(0) = (0.1, 0.1,−0.1)t .
Answer:
Matlab Code:
clc;
x1=0.1; x2=0.1; x3=-0.1; n=5;
for i=1:10
f1=(3*x1)-cos(x2*x3)-(1/2);
f2=(x1^2)-(81*(x2+0.1)^2)+sin(x3)+1.06;
f3=exp(-x1*x2)+(20*x3)+((10*pi-3)/3);
x=[x1 x2 x3]';
f=[f1 f2 f3]';
J=[3 x3*sin(x2*x3) x2*sin(x2*x3); 2*x1 -162*x2-16.2 cos(x3); x2*exp(-x1*x2)
-x1*exp(-x1*x2) 20];
x=x-(J^-1)*f;
x1=x(1); x2=x(2); x3=x(3);
disp(x)
end
Matlab Output:
0.4999
0.0193
-0.5255
0.5000
0.0016
-0.5236
0.5000
0.0000
-0.5236
0.5000
0.0000
-0.5236
0.5000
-0.0000
-0.5236
0.5000
-0.0000
-0.5236
0.5000
-0.0000
-0.5236
0.5000
0.0000
-0.5236
0.5000
-0.0000
-0.5236
0.5000
0.0000
-0.5236