I don't understand my error

close all
clear
clc

osf = 14.621;
Y = log(osf);
T = 0 : 5 : 40;
Ta = T + 273.15;

y=@(Ta) -139.34411 + (1.575701*10^5)./Ta - (6.642308*10^7)./Ta.^2 + (1.243800*10^10)./Ta.^3 - (8.621949*10^11)./Ta.^4 - Y;
g = diff(y(Ta));

Xn_0 = 274;
es = 0.5;
maxiteration = 100;

Xn = Xn_0 - ((y(Xn_0))/(g(Xn_0)));
ea = (((Xn - Xn_0)/(Xn))*100);

disp('Xn_0         y(Xn_0)          g(Xn_0)              Xn')
disp(num2str([Xn_0 y(Xn_0) g(Xn_0) Xn]));
flag = 1;

while abs (ea)>es
    Xn_0 = Xn;
    Xn = Xn_0 - y(Xn_0)/g(Xn_0);
    ea = (((Xn - Xn_0)*100)/Xn);
    
    disp(num2str([Xn_0 y(Xn_0) g(Xn_0) Xn ea]));
    
    flag = flag+1;
    if(flag == maxiteration)
        break;
    end
end

THE ERROR:

Index exceeds the number of array elements (8).

Error in Coding5 (line 17)

Xn = Xn_0 - ((y(Xn_0))/(g(Xn_0)));

Answer 1

[Image Analyst]

Name Size Bytes Class Attributes

y 1x1 32 function_handle

g 1x8 64 double

So y has 1 element and g has 8 elements. You're trying to get the 274'th element of each of these. Why?

You can't do that. Re-think what you want to do.

Answer 2

[Jan]

y = @(Ta) -139.34411 + 1.575701e5 ./ Ta - 6.642308e7 ./ Ta.^2 + 1.243800e10 ./ Ta.^3 - ...
    8.621949e11 ./ Ta.^4 - Y;
g = diff(y(Ta));

No g is not the function, which is the derivative of y, but a vector containing the differences between the neighbors. Then:

Xn = Xn_0 - y(Xn_0) / g(Xn_0);  % Avoid overdoing of parentheses

call the vector g with the index Xn_0.

I guess you want this:

% First derivative of y:
g = @(Ta) 1.575701e5 - 2 * 6.642308e7 ./ Ta + 3 * 1.243800e10 ./ Ta.^2 - ...
    4 * 8.621949e11 ./ Ta.^3;