Stability for implicit-explicit schemes for non-equilibrium kinetic systems in weighted spaces with symmetrization

TL;DR

This paper establishes stability results for implicit-explicit schemes applied to non-equilibrium kinetic systems in weighted symmetric spaces, with applications to advective and diffusive transport involving multiple species.

Contribution

It introduces stability proofs for various explicit and implicit schemes in weighted symmetric spaces for kinetic systems, including extensions to nonlinear and multi-species cases.

Findings

Proved stability of schemes in weighted symmetric spaces

Applicable to advective and diffusive transport models

Extended to nonlinear and multi-species systems

Abstract

We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include advective and diffusive transport coupled to the accumulation of immobile components governed by non-equilibrium relationships. We also discuss extensions to nonlinear relationships and multiple species.