Stability of finite difference schemes for complex diffusion processes (Q2903036)

The authors study the stability of a class of finite difference schemes for the nonlinear complex diffusion equations. The paper is organized as follows. Section 1 is the introduction. The complex diffusion equation is presented and the details on the considered class of numerical schemes are given in Section 2. The stability condition is proven. The proof for the uni-dimensional case and Neumann boundary conditions in detail are presented. The Dirichlet problem is also considered. The numerical examples are given in Section 3. The paper is ended with a Section 4 dedicated to conclusions and possible future work.