Bisection Method Code Help

Help with my code. Only spits out one value.

Function File:

%Script File:
func=@(x) sin(10*x)+cos(3*x);
xl=3; xu=5;
x=bisection1(func,xl,xu)

function root=bisection1(func,x1,xu)
xr=x1;es=.0001;
i=0;
while i<6
    i=i+1;
    xrold=xr;
    xr=(x1+xu)/2;
    if xr~=0
        ea=abs((xr-xrold)/xr)*100;
        root=xr
    else
        ea=100;
        root=xr
    end
    if func(x1)*func(xr)<0
        xu=xr;
        root=xr
        
    elseif func(x1)*func(xr)>0
        x1=xr;
        root=xr
    else
        ea=0;
        root=xr
    end
    if ea<=es,break,end
end
root=xr;
end

[David Hill]

Show us your code.

[Angelina Encinias]

Just did.

Answer 1

[Torsten]

I didn't check whether there is a programming error in bisection1. In comparison to fzero it's very inexact - that's for sure.

format long
func=@(x) sin(10*x)+cos(3*x);
xl=3.2; xu=3.3;
x(1)=bisection1(func,xl,xu);
x1(1)=fzero(func,[xl,xu]);
xl=3.3; xu=3.4;
x(2)=bisection1(func,xl,xu);
x1(2)=fzero(func,[xl,xu]);
xl=3.6; xu=3.8;
x(3)=bisection1(func,xl,xu);
x1(3)=fzero(func,[xl,xu]);
xl=4.15; xu=4.25;
x(4)=bisection1(func,xl,xu);
x1(4)=fzero(func,[xl,xu]);
xl=4.25; xu=4.35;
x(5)=bisection1(func,xl,xu);
x1(5)=fzero(func,[xl,xu]);
xl=4.5; xu=5;
x(6)=bisection1(func,xl,xu);
x1(6)=fzero(func,[xl,xu]);
x

x = 1×6

3.260937500000000 3.367187500000000 3.746875000000000 4.229687499999999 4.264062500000000 4.710937500000000

x1

x1 = 1×6

3.262423140266324 3.365992128846206 3.745745086972446 4.229067033678568 4.263590029871862 4.712388980384690

func(x)

ans = 1×6

-0.006942296312261 -0.005267769874115 0.014275699455641 -0.000954862685705 0.000745839854238 0.018868721583465

func(x1)

ans = 1×6

1.0e-14 * -0.122124532708767 0.166533453693773 0.333066907387547 -0.044408920985006 0.055511151231258 0.594077493713784

X=3:0.001:5;
plot(X,func(X))
hold on
plot(x,func(x),'o')

function root=bisection1(func,x1,xu)
xr=x1;es=.0001;
i=0;
while i<6
    i=i+1;
    xrold=xr;
    xr=(x1+xu)/2;
    if xr~=0
        ea=abs((xr-xrold)/xr)*100;
        root=xr;
    else
        ea=100;
        root=xr;
    end
    if func(x1)*func(xr)<0
        xu=xr;
        root=xr;
    elseif func(x1)*func(xr)>0
        x1=xr;
        root=xr;
    else
        ea=0;
        root=xr;
    end
    if ea<=es,break,end
end
root=xr;
end