Unrecognized function or variable 'FalsePosition'.

V=40;
rho=1.23;
D=0.005;
mu=1.79E-5;
epsilon=0.0015E-3;

Re=rho*V*D/mu;

f=@(x)(1./sqrt(x)+2*log10(epsilon./(3.7*D)+2.51./(Re*sqrt(x))));
xplot=0.008:0.001:0.08;
plot(xplot,f(xplot))
xlabel("f")
ylabel('y(f)')
grid on
a=0.008;
b=0.08;
tol=0.0001;

disp('iterNo lowerB upperB f(a) f(b) approxRoot f(r) error ')
fstats=FalsePosition(f,a,b,tol);
disp(fstats)
norows=size(fstats,1);
nocols=size(fstats,2);
froot=fstats(norows,nocols-2);

fprintf("Root by false position method =%f\n",froot);
function stats=FalsePosition(f,a,b,tol);
i=1;
iterNo=[i];
lowerB=[a];
upperB=[b];
functValueL=[f(a)];
functValueU=[f(b)];
approxRoot=[];
functValueR=[];
error=[];
if f(a)*f(b)>0
    disp('The value of f(a)*f(b)<0,choose other values of a and b')
else
    xn=f(b);
    xn_1=f(a);
    r=b-(xn*(b-a))/(xn-xn_1);
    err=abs(f(r));
    approxRoot(i)=r;
    functValueR(i)=f(r);
    error(i)=err;
    while err >tol
        i=i+1;
        iterNo(i)=i;
        if xn_1*f(r)<0
            b=r;
        else
            a=r;
        end
        r=b-(xn*(b-a))/(xn-xn_1);
        err=abs(f(r));
        upperB(i)=b;
        lowerB(i)=a;

        functValueU(i)=f(b);
        functValueL(i)=f(a);
         approxRoot(i)=r;
        functValueR(i)=f(r);
        error(i)=err;
    end
end

stats=[iterNo;lowerB;upperB;functValueL;functValueU;approxRoot;functValueR]
end

Answer 1

[Alan Stevens]

It works just fine for me! (I copied it into a script, saved the script and then clicked the Run arrow).

[Walter Roberson]

The plot shows a zero near 0.03 but the reported false position is near -0.001 . This is because the error compared to the root (last row) is being displayed instead of the position of the root (second last row)

V=40;
rho=1.23;
D=0.005;
mu=1.79E-5;
epsilon=0.0015E-3;

Re=rho*V*D/mu;

f=@(x)(1./sqrt(x)+2*log10(epsilon./(3.7*D)+2.51./(Re*sqrt(x))));
xplot=0.008:0.001:0.08;
plot(xplot,f(xplot))
xlabel("f")
ylabel('y(f)')
grid on

a=0.008;
b=0.08;
tol=0.0001;

disp('iterNo lowerB upperB f(a) f(b) approxRoot f(r) error ')

iterNo lowerB upperB f(a) f(b) approxRoot f(r) error 

fstats=FalsePosition(f,a,b,tol);
disp(fstats)

    1.0000    2.0000    3.0000    4.0000    5.0000    6.0000    7.0000    8.0000    9.0000   10.0000   11.0000   12.0000   13.0000   14.0000   15.0000
    0.0080    0.0080    0.0080    0.0080    0.0234    0.0284    0.0284    0.0284    0.0284    0.0288    0.0288    0.0290    0.0290    0.0290    0.0290
    0.0800    0.0570    0.0413    0.0307    0.0307    0.0307    0.0299    0.0294    0.0291    0.0291    0.0290    0.0290    0.0290    0.0290    0.0290
    5.8343    5.8343    5.8343    5.8343    0.7447    0.0720    0.0720    0.0720    0.0720    0.0137    0.0137    0.0012    0.0012    0.0012    0.0012
   -2.7416   -1.9559   -1.0987   -0.1884   -0.1884   -0.1884   -0.1083   -0.0522   -0.0132   -0.0132   -0.0046   -0.0046   -0.0028   -0.0015   -0.0006
    0.0570    0.0413    0.0307    0.0234    0.0284    0.0299    0.0294    0.0291    0.0288    0.0290    0.0290    0.0290    0.0290    0.0290    0.0290
   -1.9559   -1.0987   -0.1884    0.7447    0.0720   -0.1083   -0.0522   -0.0132    0.0137   -0.0046    0.0012   -0.0028   -0.0015   -0.0006   -0.0000

norows=size(fstats,1);
nocols=size(fstats,2);
froot=fstats(norows,nocols-2);

fprintf("Root by false position method =%f\n",froot);

Root by false position method =-0.001498

function stats=FalsePosition(f,a,b,tol);
i=1;
iterNo=[i];
lowerB=[a];
upperB=[b];
functValueL=[f(a)];
functValueU=[f(b)];
approxRoot=[];
functValueR=[];
error=[];
if f(a)*f(b)>0
    disp('The value of f(a)*f(b)<0,choose other values of a and b')
else
    xn=f(b);
    xn_1=f(a);
    r=b-(xn*(b-a))/(xn-xn_1);
    err=abs(f(r));
    approxRoot(i)=r;
    functValueR(i)=f(r);
    error(i)=err;
    while err >tol
        i=i+1;
        iterNo(i)=i;
        if xn_1*f(r)<0
            b=r;
        else
            a=r;
        end
        r=b-(xn*(b-a))/(xn-xn_1);
        err=abs(f(r));
        upperB(i)=b;
        lowerB(i)=a;

        functValueU(i)=f(b);
        functValueL(i)=f(a);
         approxRoot(i)=r;
        functValueR(i)=f(r);
        error(i)=err;
    end
end

stats=[iterNo;lowerB;upperB;functValueL;functValueU;approxRoot;functValueR];
end