PDE solution with the Shampine coefficients.

Presented below is a solution to the heat equation using the Shampine coefficients for the Rosenbrock algorithm, with the following partial differential equation:

   

The initial & boundary conditions are as follows:

                               

The method of lines was used to convert the PDE’s to a familiar form of the ODE’s so as to allow easy implementation with the generalized Rosenbrock formulation. The slab of length 1 unit was divided into 20 segments. Plotted below is the temperature distribution over the slab, as a function of time.