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Thread: Bisection Method for Engineering Beam Problems - Matlab

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    Member kotov9syndrome is on a distinguished road kotov9syndrome's Avatar
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    Default Bisection Method for Engineering Beam Problems - Matlab

    Does anyone know how to use matlab to do bisection methods for numerical methods???

    Please help.

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    Senior Member nslay has a reputation beyond repute nslay has a reputation beyond repute nslay has a reputation beyond repute nslay has a reputation beyond repute nslay has a reputation beyond repute nslay has a reputation beyond repute nslay has a reputation beyond repute nslay has a reputation beyond repute nslay has a reputation beyond repute nslay has a reputation beyond repute nslay has a reputation beyond repute nslay's Avatar
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    Default Re: Bisection Method for Engineering Beam Problems - Matlab

    Quote Originally Posted by kotov9syndrome View Post
    Does anyone know how to use matlab to do bisection methods for numerical methods???

    Please help.
    [s]Which do you understand the least? The theory behind the bisection method, or the matlab scripting?[/s]

    EDIT:
    Matlab might have a better root solver than bisection. Here's my octave implementation

    Code:
    function [x,nsteps] = bisect(func,a,b,epsilon)
    
    funcstr = ['y=',func,';'];
    
    x = a;
    eval(funcstr);
    ya = y;
    
    x = b;
    eval(funcstr);
    yb = y;
    
    % Does it satisfy the intermediate value theorem?
    if (ya > 0 & yb > 0) | (ya < 0 & yb < 0)
            % Nope
            nsteps = -1;
            return;
    end
    
    % From mathworld
    nsteps = ceil(log2(b-a)-log2(epsilon));
    
    for i=1:nsteps
            mid = 0.5*(a+b);
    
            x = mid;
            eval(funcstr);
            ymid = y;
    
            % Does the first bisected interval satisfy the intermediate value theorem?
            if (ymid > 0 & ya < 0) | (ymid < 0 & ya > 0)
                    b = mid;
                    yb = ymid;
            else
                    % Nope, so it must be the second interval
                    a = mid;
                    ya = ymid;
            end
    end
    
    x = 0.5*(a+b);
    Example use:
    Code:
    octave-3.2.4.exe:30> [y,nsteps] = bisect("x^2-2",1,2,1e-16)
    y =  1.4142
    nsteps =  54
    octave-3.2.4.exe:31> [y,nsteps] = bisect("x^2-2",2,5,1e-16)
    y =  5
    nsteps = -1
    You may have to tweak it a little for Matlab.
    Last edited by nslay; 03-10-2014 at 07:45 PM.

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