You are indeed a blessing to humanity and scientific world'!!!,
Lastly, it seems to me that the coupled equations have analytical solutions
(1) I need the numerical values of the analytical solutions of B(x, t) and C(x, t)
(2) if the numerical values of the analytical results of B(x, t) and C(x,t) is subtracted from the approximate results you got, I need the tabulated error values.
(3) lastly, the plots of the behavior of the Numerical results (error analysis) is needed. thanks.
@tomleslie