MATLAB: Need help creating a function m-file for the bisection method for the following equation…

bisectionbisection methodmechanical

I'm really stuck on an assignment that regards the bisection method. This is due to me missing all of my lectures for the module because I have transferred course from Chemical to Mechanical Engineering. I can't get help from within the University as it is outside of term-time now and I am back home.

I am having great difficulty with the following task for which I have been given these values:

k = 1; n = 0.6833; U = 1.0714; Pgrad = -3.333333…..

I am then given the following equation defining the pressure gradient in a pipe of radius 'R' (the only unknown in the equation):

Pgrad = -2k * ( ( U * (3n + 1) ) / ( n * R ^ (1 + 1/n) ) ) ^ n
Use the bisection method to determine an approximate value of R, with an absolute error of less than 1 x 10^-6.

I'm not expecting someone to come up with the whole m-file or anything, but any help whatsoever would be greatly appreciated. I've spent hours and hours trying to catch up with where I should be on the course and even resorted to watching videos on Youtube to see if any could help.

Even if people could just try and point me in the right direction.

Thanks

(Here is the question from the actual assignment sheet)

Best Answer

I recommend you carefully read the Wikipedia article at:

http://en.wikipedia.org/wiki/Bisection_method

The method requires that you first find two values a and b such that the function f(R ) whose root you are attempting to find has opposite signs for f(a) and f(b). For that purpose I advise you to make a plot of your f(R ) with varying R so you can see approximately where it crosses the zero point and thus how to set those initial starting values for a and b. For your looping until the error is less than 1e-6, you will need to use matlab's 'while' command to continue until that condition is satisfied. The above article gives a fairly clear description of how to proceed within the while-loop.

In Mathworks' File Exchange there are several contributions whose codes could possibly guide you to a solution if you get desperate. See the list at:

 http://www.mathworks.com/matlabcentral/fileexchange/index?term=bisection&utf8=✓

Related Solutions

MATLAB: Bisection help PLS HELP ME

"but I cant seem to figure out why it wont work I just get this error"

function f_value=f(~)
k = 2800;
m = 0.6705;
Fo = 2.0535;
t = 9.177;
x = 0.0253;
w = 77:0.1:80;
wn= sqrt(k/m);
fo= Fo/m;
x=(2*Fo/wn^2-w.^2).*sin((wn-w./2)*t).*sin((wn+w./2).*t);
f_value = x;
end

Main Script:

    clc
    clear all;
    close all;
    % approximate solution to an equation.
    % The number of bisection steps
    n = 32;
    % define the initial interval
    a = 41;
    b = 69;
    fprintf('\n initial interval [%g, %g] \n total bisection steps %d\n', a,b,n);
    % Check that a root does exist in the chosen interval
    x_left = a;
    x_right = b;
    f_left=f(x_left);
    f_right=f(x_right);
    if (f_left.*f_right)> 0
    end
    % Bisection: The method
    for i=1:n
        if f_left == 0
            % The exact root of the equation is found at the lower bound
            % of the chosen interval

            fprintf('\n stage %g root %g with zero absolute error \n',i,x_left);
            return;
        end
        if f_right==0
            % The exact root of the equation is found at the upper bound
            % of the chosen interval
            fprintf('\n stage %g root %g with zero absolute error \n',i,x_right);
            return
        end
        % Bisection method: The 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
        % Calculate the approximate root for current step
        root = (x_left+x_right)/2.0;
        % Calculate the absolute error for current 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);

Command Window:

Please note: I removed the code errors only.

MATLAB: Error using function matlab

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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