Index exceeds matrix dimensions (Thermal 1d model)

I'm trying to write a 1D thermal model using a finite difference scheme. I'm still an amateur programmer so I apologize for my ignorance. I keep getting this error: Index exceeds matrix dimensions. I know this means that I'm trying to access an element in an array using an index that exceeds the dimension of the array but I don't know what to do with that information.

N = 15;
% Geometrically increasing grid spacing
z = 0;
zs = [kappa*P/pi]^(1/2);
deltaz = zs/10;
for i = 1:N
deltaz(i+1) = deltaz(i)*(1+1/5);
z(i+1) = z(i)+deltaz(i);
T0 = [[(S0/R^2).*(1-A)]/(e*(5.67*10^-8))]^(1/4);
TN = T0/((2)^(1/2));
T(i+1) = TN - (TN-T0)*exp(-z(i+1)/0.06);
zor(i+1) = deltaz(i+1)*deltaz(i)*(deltaz(i+1)+deltaz(i));
alpha_model(i+1) = 2*K*deltaz(i+1)/zor(i+1);
beta_model(i+1) = 2*K*deltaz(i)/(zor(i+1));
  for n= 1:N
  T(i+1,n+2) = T(i+1,n+1) + [dt/(rho*cp)].*[alpha_model(i+1).*T(i,n+1)-(alpha_model(i+1) + beta_model(i+1)).*T(i+1,n+1) + beta_model(i+1).*T(i+2,n+1)];
  end
end

[Jan]

Start with posting the complete message. Then the readers do not have to guess, which line is failing.

We cannot run your code, because

zs = [kappa*P/pi]^(1/2);

is failing due to unknown kappa. By the way:

zs = sqrt(kappa * P / pi);

is nicer and faster. Do not use square brackets without any reasons. See https://www.mathworks.com/matlabcentral/answers/35676-why-not-use-square-brackets . [] is the concatenation operator.

Answer 1

[Jan]

You define

T(i+1) = TN - (TN-T0)*exp(-z(i+1)/0.06);

but access

T(i+1, n+1)

[Aditya Khuller]

Thank you for your help!