My work is situated in the context of numerical simulation of physical phenomena. However, simulating complex systems involving multiple interacting physical processes is a major challenge. The literature in numerical analysis has provided many advances in the numerical integration of partial differential equations (PDEs) and ordinary differential equations (ODEs), which has enabled the development of numerous computational codes simulating a wide range of phenomena.

In the case of multiphysics simulations, it is advantageous to take advantage of solvers that have already been validated by the scientific community rather than rewriting monolithic codes that incorporate all equations at once. This so-called partitioned approach aims to construct a procedure (i.e., a numerical scheme) that enables the numerical coupling of different computational codes.

This approach raises many mathematical issues (order of convergence, stability, accuracy, etc.) as well as computational challenges (such as scalability in high-performance computing). My thesis focuses on a new high-order multistep coupling scheme. My presentation will focus on describing the method in both its implicit and explicit variants, as well as on analyzing its stability.