Fast stable finite difference schemes for nonlinear cross-diffusion.

• The dynamics of cross-diffusion leads to a high complexity on implicit finite difference schemes implementations. • Two stable operator splitting schemes are proposed to lower the complexity. • A stable factorization of the system matrix is derived to fasten the computations. • We achieve competitive running times (similar to explicit approaches) for these implicit implementations. The dynamics of cross-diffusion models leads to a high computational complexity for implicit difference schemes, turning them unsuitable for tasks that require results in real-time. We propose the use of two operator splitting schemes for nonlinear cross-diffusion processes in order to lower the computational load, and establish their stability properties using discrete L 2 energy methods. Furthermore, by attaining a stable factorization of the system matrix as a forward-backward pass, corresponding to the Thomas algorithm for self-diffusion processes, we show that the use of implicit cross-diffusion can be competitive in terms of execution time, widening the range of viable cross-diffusion coefficients for on-the-fly applications. [ABSTRACT FROM AUTHOR]