Bisection method for transcendental equations. I:e tan(x)= x

clear all

clc

f = @(x) tan(x) - x;

x1 = p;

x2 = (3*pi)/2;

if f(x1)*f(x2) < 0

fprintf('No routes');

end

if f(x1) == 0;

fprintf('pi/2 is one of the roots')

return

elseif f(x2) == 0;

fprintf('3*pi/2 is one of the roots')

return

end

while abs(f(x1)) < 0.0001

xmid = (x1+x2)/2; %bisection

if f(x1)*f(xmid) < 0

x2 = xmid;

else

x1 = xmid;

end

end

fprintf('The root is: %f%d\n',x1)

syms y

s = vpasolve(tan(y) == y,y,[pi/2,(3*pi)/2])

I feel like my loop is incorrect and the output I am getting is incorrect, Ive looked at other bisection method examples here on mathworks but I can get it to work for my specific case.

Answer 1

[Alan Stevens]

If I were you I would change the "while" condition to

while abs(x1-x2) > 0.0001

[Alan Stevens]

Also, where you have

if f(x1)*f(x2) < 0
    fprintf('No routes');
end

you should have

if f(x1)*f(x2) > 0
    fprintf('No roots');
end

(The important part being the > sign!)