Consider the method of lines solutions of the unsteady reaction–diffusion equation with a second-order bulk reaction,

with an initial concentration c = 0 and boundary conditions c(0) = 1 and ∂c/∂x = 0 at x = L. Answer the following questions.

(a) If we discretize with centered finite differences and use an explicit Euler equation, what are the equations we need to solve to compute c_i^(k) at each node i and time step k?

(b) If we instead use implicit Euler, what are the residuals and Jacobian for the nonlinear system?

Transcribed Image Text:

ас at а²с = D- ах2 - kc²