2023/11/20 by Marco Caliari, Fabio Cassini · 11 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Advection #Algorithm #Applied mathematics #Brusselator #Computation #Differential equation #Dimension (graph theory) #Exponential function #Integrator #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix exponential #Model Reduction and Neural Networks #Nonlinear system #Numerical methods for differential equations #Physics #Reaction–diffusion system
paper · doi:10.1016/j.jcp.2023.112640
published in Journal of Computational Physics 498, 112640 (Elsevier BV)
openalex publication_date 2023/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection–diffusion–reaction equations in two and three space dimensions. It is based on a directional splitting of the involved matrix functions, which allows for a simple yet efficient implementation through the computation of small-sized exponential-like functions and tensor-matrix products. The procedure straightforwardly extends to the case of an arbitrary number of components and to any space dimension. Several numerical examples in 2D and 3D with physically relevant (advective) Schnakenberg, FitzHugh–Nagumo, DIB, and advective Brusselator models clearly show the advantage of the approach against state-of-the-art techniques.