2019/05/08 by Nadia Loy, Loy, N., Mattia Zanella +1 · 1 citation
Environmental Science · Physics and Astronomy · #35Q70 #35Q84 #65N06 #Adaptation and Self-Organizing Systems (nlin.AO) #Climate variability and models #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Opinion Dynamics and Social Influence #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1905.02970
openalex publication_date 2019/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we consider an extension of a recently proposed structure preserving numerical scheme for nonlinear Fokker-Planck-type equations to the case of nonconstant full diffusion matrices. While in existing works the schemes are formulated in a one-dimensional setting, here we consider exclusively the two-dimensional case. We prove that the proposed schemes preserve fundamental structural properties like nonnegativity of the solution without restriction on the size of the mesh and entropy dissipation. Moreover, all the methods presented here are at least second order accurate in the transient regimes and arbitrarily high order for large times in the hypothesis in which the flux vanishes at the stationary state. Suitable numerical tests will confirm the theoretical results.