newton.m

%NEWTON finds the real zeros of the function y.
%       NEWTON finds real zeros by an interactive Newton procedure.
%       Uses the M-file ITERMENU.


tol = 0.00001;
disp('Enter the equation to be solved, y(x), and the derivative')
disp('of y with respect to x as strings variables, for example:')
disp('y    = ''x - sin(x) - c''')
disp('dydx = ''1 - cos(x)''')
disp('When the program returns the prompt k enter the appropriate')
disp('escape command to exit keyboard mode and continue the program.')
keyboard
disp('Enter now the range within which you want to plot the equation.')
disp('Then, after viewing the plot press any key to continue')
xmin = input('x min = ')
xmax = input('x max = ')
xx = xmin: (xmax-xmin)/100: xmax;
z = zeros(1, 100);
for k = 1:101
        x     = xx(k);
        yy    = eval(y);
        z(k)  = yy;
end
plot(xx, z)
grid
title('Plot of the equation to be solved')
xlabel('x')
ylabel('y(x)')
pause
real_zeros = [ ];       % initialize array of real zeros
itermenu
answer = input('Enter your choice')
while answer ~= 3
       if answer == 1
              xmin = input('x min = ')
              xmax = input('x max = ')
              xstep = (xmax - xmin)/100;
              xx = xmin: xstep: xmax;
              z = zeros(1, 100);
              for k = 1: 101
                     x = xx(k);
                     yy = eval(y);
                     z(k) = yy;
              end
              plot(xx, z)
              grid
              xlabel('x')
              ylabel('y')
              pause
              itermenu
              answer = input('Enter your choice')
       elseif answer == 2
              disp('Enter initial guess')
              [ x, yg ] = ginput(1)
              for l = 1:100
                     x0 = x;
                     x  = x0 - eval(y)/eval(dydx)
                     if abs(x - x0) < tol
                             break
                     end
              end
              if (l == 100)&(abs(x - x0) >= tol)
                     disp('Procedure did not converge')
              else
                     real_zeros = [ real_zeros x ];
              end
              itermenu
              answer = input('Enter new choice')
      else
              if answer ~= 3
                     disp('Incorrect answer, please repeat')
                     itermenu
                     answer = input('Enter new choice')
              end
       end
end