Why am I getting this error and how can I fix it?

*the following is saved as a file/script f1.m

function F = f1(x)
F(5) = x(5)^3+2*x(-1)^2-10;
F(-1) = x(5)*x(-1)-2;

*when I type the following in the command window,

x0 = [1 1]; 
options=optimset('Display','iter'); 
x = fsolve('f1',x0,options)

*But I get the following error

??? Attempted to access x(5); index out of bounds because
numel(x)=2.

Error in ==> f1 at 9
F(5) = x(5)^3+4*x(-1)^2-10;

Error in ==> fsolve at 254
            fuser = feval(funfcn{3},x,varargin{:});

Caused by:
    Failure in initial user-supplied objective function
    evaluation. FSOLVE cannot continue.

-- * Any help at all is much appericated, thank you.

Answer 1

[Youssef Khmou]

F is 2x1 vector so as the input x, the starting points are set in x0, and F(-5) has no sense because the index of vector starts at 1 .

function F = f1(x)
F(1)  = x(1)^3+2*x(2)^2-10;
F(2)  =  x(1)*x(2)-2;
%-----------------------
x0=[5 -1];
options=optimset('Display','iter');
x = fsolve('f1',x0,options)

[Sabbir]

Thank you so much Youssef!

Answer 2

[Walter Roberson]

You set x0 to [1 1], so a vector of length 2 will be passed in to f1. But in f1, you expect the vector to be length 5.

You are also going to have problems because your code includes x(-1) which is a request to access location negative 1 of the array "x". Arrays must be indexed by non-negative integers.

Notice too that you assign your outputs to F(5) and F(-1) . fzero() expects a single scalar as output.

Are you possibly trying to code a recursion equation ?

[Sabbir]

Thank you for the quick response. I was trying to solve the 2 non-linear equations with starting points x1=5 and x2=-1. Also to find the number of iterations used to find my solution.

I am not sure where to go with this as I am stuck.

[Walter Roberson]

Please write out the equations you are trying to solve and indicate which parts are known and which parts are unknown.

[Sabbir]

Solve the following non linear equations f(x1,x2)= (x1)^3+2*(x2)^2-10=0 and f(x1,X2)=(x1*x2)-2=0; Use starting points x1=5 and x2=-1. Also find the number of iterations MATLAB used to find the solution.

[Sabbir]

Thank you Walter as well.