MATLAB: Error using function matlab

bisection methodMATLAB

Hi, I’m trying to use the bisection method to find x. Think there’s a problem using the function. If you have any hints to help me fix it, it would be much appreciated. Thanks 
clc
k=1007.564; %stiffness (N/m)
m=98.668; %mass (kg)
F_0=108.764; %applied force magnitude (N)
x_0=-0.02; %initial displacement (m)
v_0=0.1; %initial velocity (m/s)
t=4.54; %time (s)
x_1=0.0386; %displacement (m)
om_n=sqrt(k/m);
f_0=F_0/m;
x=0; %omega
function bisection
    n = 20;
    % initial interval
    a = 5.12;
    b = 6.45;
    fprintf('\n initial interval [%g, %g] \n total bisection steps %d\n', a,b,n);
    
    %initialise and check that there is a root in the prescribed interval
    x_left = a;
    x_right = b;
    f_left = f(x_left);
    f_right = f(x_right);
    if f_left*f_right > 0
        error('ERROR: no root in the specified interval');
    end
    %the bisection method
    for i=1:n
        if f_left == 0
            %exact root is reached by the left bound of the interval
            fprintf('\n stage %g root %g with zero absolute error \n',i,x_left);
            return;
        end
        if f_right==0
            %exact root is reached by the right bound of the interval
            fprintf('\n stage %g root %g with zero absolute error \n',i,x_right);
            return
        end
        %the bisection process
        x_mid = (x_left+x_right)/2.0;
        f_mid = f(x_mid);
        if f_left*f_mid <= 0
            %there is a root in [x_left,x_mid]
            x_right = x_mid;
            f_right = f_mid;
        end
        if f_left*f_mid > 0
            % there is a root in [x_mid,x_right]
            x_left = x_mid;
            f_left = f_mid;
        end
        %compute the approximate rood for the current bisection step
        root = (x_left+x_right)/2.0;
        %compute the absolute error for the current bisection step
        abs_err=(x_right-x_left)/2.0;
        fprintf('\n stage %g root %g absolute error < %g \n',i,root,abs_err);
    end
    %check satisfaction of equation at end of process
    residual = f(root);
    fprintf('\n final residual = %g \n',residual);
end
%Subfunction defines the equation f(x) = 0
function f_value = f(x) %x=omega
    f_value = (v_0/om_n)*sin(om_n*t) + (x_0-((f_0)/(om_n)^2-(x)^2))*cos(om_n*t) + ((f_0)/(om_n)^2-(x)^2)*cos(x*t);
end

Best Answer

You do not call the function bisection
Your function f does not have access to the variables defined in the script. f would need to be a nested function using shared variables -- and you need to nest inside a function, not inside a script.
For example,
function driver
    k=1007.564; %stiffness (N/m)
    m=98.668; %mass (kg)
    F_0=108.764; %applied force magnitude (N)
    
    bisection(@f);      %call your function
    
    function f_value = f(x) %x=omega
        %this is a nested function that shares variables
      f_value = (v_0/om_n)*sin(om_n*t) + (x_0-((f_0)/(om_n)^2-(x)^2))*cos(om_n*t) + ((f_0)/(om_n)^2-(x)^2)*cos(x*t);
    end
end
function bisection(f)
  stuff
end
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