What does the error Attempted to access k(3e-10); index must be a positive integer or logical. mean?

Here is my code :-

M = 20; %number of iterations
a= 2*(10^(-10));
b= 1*(10^(-10));
U0=9;
kstart = -pi/(a+b); %Starting point
kstop = pi/(a+b);   %Stop point

delta_k = (kstop - kstart)/M; %Discretization step

for n=0:1:M           %begin cycle

      k = kstart + n*delta_k;
      k1(n+1) = k;
      fun = @(x) (((1-2*x)./(2*sqrt(x.*(1-x)))).*sin(pi*sqrt(x))).*sinh(pi*sqrt(1-x)) + cos(pi*sqrt(x)).*cosh(pi*sqrt(1-x)) - cos(k(a+b));
      x0 = 0.3;   % Initial estimate to the solution
      Sol = fzero(fun,x0);     %Solve a generic equation Sin(2x) = Cos(k) numerically
      Sol1(n+1) = Sol;
      Sola = fzero(fun,1.0);     %Solve a generic equation Sin(2x) = Cos(k) numerically
      Sol2(n+1) = Sola;
      Solb = fzero(fun,2.0);     %Solve a generic equation Sin(2x) = Cos(k) numerically
      Sol3(n+1) = Solb;
      E = Sol*U0;
      E1(n+1) = E;
      Ea = Sola*U0;
      E2(n+1) = Ea;
      Eb = Sol*U0;
      E3(n+1) = Eb;
      formatSpec = 'Counter i = %1.0f; Wavenumber k = %1.2f; Solution_1 = %1.5f\n; Solution_2 = %1.5f\n; Solution_3 = %1.5f\n; Energy_1= %1.5f\n; Energy_2= %1.5f\n; Energy_3= %1.5f\n ';
      fprintf(formatSpec,n,k,Sol,Sola,Solb,E1,E2,E3) %Print the solution

end
figure
plot(k1,E1,'g')  %Plot the graph using the vectors of numerical values as above
hold on
plot(k1,E2,'b')
hold on
plot(k1,E3,'r')
axis([-1.1*(10^10) 1.1*(10^10) 0 5])
xlabel('wavenumber')
ylabel('Energy eV')

Error using fzero (line 289)
FZERO cannot continue because user supplied function_handle ==>
@(x)(((1-2*x)./(2*sqrt(x.*(1-x)))).*sin(pi*sqrt(x))).*sinh(pi*sqrt(1-x))+cos(pi*sqrt(x)).*cosh(pi*sqrt(1-x))-cos(k(a+b))
 failed with the error below.

   Attempted to access k(3e-10); index must be a positive integer or logical.

[Star Strider]

It means that 3e-10 is not an integer greater than zero.

Array indices can be either integers greater than zero, or logical arrays.

See: Matrix Indexing (link) for details.

[Judith Tan]

I see. Thanks a lot.

[Star Strider]

My pleasure.

Answer 1

[Christoph F.]

k(a+b)

means to MatLab "the (a+b)th element of vector k". However, a+b isn't integer.

Maybe the expression

cos(k(a+b))

is missing an operator somewhere?

[Judith Tan]

Yes, it is. Thank you very much. I didn't quite understand the error.