The error means your are trying to index an element of your array that does not exist. The error is telling you that your array only contains 1 element, so your index is >1.
Here, xu and xl both start as scalars. Your if statement adds an ith value to only one of the vectors, so at any given time, one will have i elements, and the other can only have at most i-1 elements. However, the line of code throwing the error assumes they both have i elements.
You also index i twice - once at the top of your while loop, and again at the bottom.
I had to add som '.^' to your r_bisection equation to address a new error.
You will need to update your code to fix these issues. Here's a first pass:
clc;
clear all;
close all;
%Mini Project
%Bisection Method
syms f(x);
f(x)=(-4.868e-7)*(4*x^3)+(1.496e-4)*(3*x^2)+(-0.0094)*(2*x)+(-0.3324);
i=1;
xl(i)=-200;
xu(i)=200;
xr(i)=(xl(i)+xu(i))/2;
if f(xr(i))~=0
while i<100
i=i+1;
if f(xl(i-1))*f(xr(i-1))<0
xu(i)=xr(i-1);
fu(i)=f(xr(i-1));
xl(i)=0;
fl(i)=0;
else
xl(i)=xr(i-1);
fl(i)=f(xr(i-1));
xu(i)=0;
fu(i)=0;
end
xr(i)=(xu(i)+xl(i))/2;
if i>1
ea=abs((xr(i)-xr(i-1))/xr(i))*100;
if ea<0.05
break;
end
end
% i=i+1;
end
end
figure(1)
plot(i,ea)
hold on
grid on
xlabel('Iteration')
ylabel('Percent Approximation Error')
y=-200:10:200;
figure(2)
hold on
grid on
box on
for i=1:1:length(y)
plot(y,f(y),'LineWidth',2)
end
plot(xr,f(xr),'*','MarkerSize',10);
xlabel('Temperature (K)')
ylabel('Derivative of f(T)')
yline(0);
r_bisection=(-4.868e-7)*(xr.^4)+(1.496e-4)*(xr.^3)+(-0.0094)*(xr.^2)+(-0.3324*xr)+14.55;
et=abs((-13.2493-xr)/-13.2493)*100;
