Stability Analysis of high order discrete boundary conditions with Inverse Lax Wendroff method

I will present my PhD subject which is about numerical analysis. More precisely, I study finite difference schemes with boundary and initial data and I will present the Inverse Lax Wendroff procedure which is used to construct ghost points at the inflow boundaries. I will introduce also the Simplified Inverse Lax Wendroff procedure which mixes Inverse Lax Wendroff procedure and extrapolation at the boundary. The accuracy and the stability features of the global procedure are fundamental. Therefore, I will use the GKS theory and pseudo spectral properties of Quasi-Toeplitz operator to handle the stability analysis and explicit multiscale expansions to estimate the possible discrete boundary layers that may limit the accuracy.