How can I plot this function using Brent's method?

in the interval (0:0004; 0:0012).

Answer 1

[Manoj Kumar Koduru]

f=@(u) u*(1+0.7166/cos(25*sqrt(u)))-1.6901e-2; %Equation 
a=-10;
b=+10;
err=0.001;
%Testing root is bracketed between [a b]
if f(a)*f(b) >=0
    opts=struct('WindowsStyle','model','Interpreter','tex');
    F=errordlg('The Root is out of the Brackets,increase a and b values'....
        ,'Roots Are Not Bracketed',opts); %Message Box
end
%Swapping a and b Contents
if abs(f(a)) < abs(f(b))
    L=a; a=b; b=L;
end
c=a;
MFlag=1;
%Main Loop
delta =err; i=0;
while abs(b-a) >=err
    i=i+1;
    if f(a) ~=f(c)&&f(b) ~=f(c)
        s=a*f(b)*f(c)/(f(a)-f(b))*(f(a)-f(c))+....
            b*f(a)*f(c)/((f(b)*f(a))*(f(b)-f(c)))+...
            c*f(a)*f(b)/((f(c)-f(a))*(f(c)-f(b))); %Inverse Quadratic Interpolation
    else
        s=b-f(b)*(b-a)/(f(b)-f(a));  %Secant method
    end
    if s<=(3*a+b)/4 || s>=b ||....
            (MFlag==1 && abs(s-b) >= abs(b-c)/2) ||....
            (MFlag==0 && abs(s-b) >= abs(c-d)/2) ||....
            (MFlag==1 && abs(b-c) < abs(delta)) ||....
            (MFlag==0 && abs(c-d) >= abs(delta))
        s=(a+b)/2;  %Bisection Method
        MFlag=1;
    else
        MFlag=0;
    end
    %Calculate f(s)
    d=c; c=b;
    if f(a)*f(s) <0
        b=s;
    else
        a=s;
    end
    %Swapping a and b contents
    if abs(f(a)) < abs(f(b))
        if abs(f(a)) < abs(f(b))
        L=a; a=b; b=L;
        end
    end
    ss(i,1)=s;
    dd(i,1)=d;
    ii(i,1)=i;
end

plot(1:i,ss,'Linewidth',2);
grid on
title('Brent Method')
xlabel('Number of Itterations')
ylabel('Root Contents')

[Boran Kolcu]

Thank you so much!

[John D'Errico]

Please don't do obvious homework problems for students. They learn nothing from you, except to then post every homework question here.