Question

Write a User Defined Function in Matlab solve for the roots of a function using bisection method. The user provides two variables for the function to test and bisect if needed.

Answer 1

CODE

function root= bisection(fun, lb, ub,iter_max, Emax)
flb=fun(lb); % find the f(lb) value
fub=fun(ub); % find the f(ub) value
i=0; % the initial iteration
%Check if you have already found the solution
if flb==0
root=lb;
fprintf('The root is: %5.3f \n', root)
return
end
if fub==0
root=ub;
fprintf('The root is: %5.3f \n', root)
return
end
%now to test if there is a root within the uppper and lower limits
if flb*fub>0
disp('termination type 1: there is no root within bracket')
root=NaN;
return
end
%solution guess
root= (lb+ub)/2;
for i=1:iter_max
rootPrevious=root;
fxr=fun(root);
if i >= iter_max
disp('termination type 0: algorithm terminated due to maximum interations')
break
elseif fxr==0 % test if this is the case where root is directly the root
disp('this is the root')
break
end
% if none of above is met, then process the commands below
if fxr*flb>0
lb=root;
else
ub=root;
end
root= (lb+ub)/2;
error=abs((root-rootPrevious)/root);
if error<Emax
break
end
end
fprintf('The iterations taken is: %d \n', i)
fprintf('The root is: %5.3f \n', root)