Solve heat equation with source term

I have a system of coupled PDEs relatd to the heat equation that I am trying to solve using the 'pdepe' command in Matlab. The equations are as follows-

Here, 'T' and 'm' are the independent variables and 't' is time. A(m, T) is a function of both 'm' and 'T' while k(T) is a function of T only. B is a constant. The initial conditions are as follows-

(T0 is a constant)

The boundary conditions are-

,

,

I know how to use pdepe when only one independent variable is there but with two I am having trouble casting these equations in the matrix form that is expected by the solver. Any help is appreciated!

Answer 1

[Bill Greene]

T and m are referred to as dependent variables, not independent; x and t are the independent variables. This Example shows how to use pdepe for a problem with two dependent variables. To satisfy the requirements for pdepe input, you will need to substitute your second equation into the first to eliminate .