Page 87 - Numerical Analysis Using MATLAB and Excel

Chapter 2 Root Approximations

% Finding roots by Newton's method
% The following is the first derivative of
% the function defined as exercise3
y=−2.*sin(2.*x)+2.*cos(2.*x)+1;
Now, we write and execute the following program and we find that the second root is

x = 2.2295 and this is consistent with the value shown on the plot.

x = input('Enter starting value: ');
fx = exercise3(x);
fprimex = exercise3der(x);
xnext = x−fx/fprimex;
x = xnext;
fx = exercise3(x);
fprimex = exercise3der(x);
disp(sprintf('First approximation is x = %9.6f \n', x))
while input('Next approximation? (<enter>=no,1=yes)');
xnext=x−fx/fprimex;
x=xnext;
fx=exercise3(x);
fprimex=exercise3der(x);
disp(sprintf('Next approximation is x = %9.6f \n', x))
end;
disp(sprintf('%9.6f \n', x))
Enter starting value: 3

First approximation is x = 2.229485

2−34 Numerical Analysis Using MATLAB® and Excel®, Third Edition
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