There are several problems with this code.
These two lines are unnecessary. Often people put them in because they've seen them in others' scripts but they can impede the ability to debug the code efficiently.
[t,T] = ode15s(@(t,T) dTdt, tspan, y0);
Nowhere in this code do you define a function named dTdt that accepts 0 input arguments and returns the value of the right-hand side of your system of ODEs. If you want this to call your function named odeFunc with two inputs use either:
[t,T] = ode15s(@(t,T) odeFunc(t, T), tspan, y0);
or
[t,T] = ode15s(@odeFunc, tspan, y0);
k4(i,j)= lambda(i,j)/r(i,j)*(delr)*(rho)*(Cp);
function dTdt = odeFunc(t,T)
Nowhere in this function are variables i or j defined, so MATLAB will use the values returned by the i and j functions. This will error because you can't assign to the sqrt(-1)th row or column of a matrix. Yes, you defined the i and j variables before you called ode15s but that is a separate workspace. Since you didn't pass the i and j variables into the function call's workspace, they're not visible in the function call's workspace. [I'm ignoring nested functions and global variables for purpose of this explanation.] Again, since you didn't pass delr into this function's workspace, it's not visible. For ways to pass additional parameters into the function see this documentation page. dTdt(i,j) = k*(Tin(i,j)-k*T(i,j))+(k4(i,j))*T(i,j+1))-k4(i,j)*T(i,j);
As @VBBV stated, you have an extra ) in your code. If you're editing this in the MATLAB Editor, Code Analyzer should have flagged this line. Indeed, it flags the second ) after T(i,j+1) as well as the other ) following it on the line. As for the other message you listed, check that you haven't created a script file ode15s.m. If you have, rename it. The following command should only list files under matlabroot.
