Stability analysis of CrankNicolson and Euler schemes for time-dependent diffusion equations
In this paper, we study the stability of the CrankNicolson and Euler schemes for time-dependent diffusion coefficient equations on a staggered grid with explicit and implicit approximations to the Dirichlet boundary conditions. Using the matrix representation for the numerical scheme and boundary conditions it is shown that for implicit boundary conditions the CrankNicolson scheme is unrestrictedly stable while it becomes conditionally stable for explicit boundary conditions. Numerical examples are provided illustrating this behavior. For the Euler schemes the results are similar to those for the constant coefficient case. The implicit Euler with implicit or explicit boundary conditions is unrestrictedly stable while the explicit Euler with explicit boundary conditions presents the usual stability restriction on the time step.
stability analysis staggered grids boundary conditions cranknicolson scheme non-constant coefficient diffusion equations 65m06 65m12 65m99