High Order PDE-Convergence: ADI-Type Integrators

This lecture discusses the convergence of high-order partial differential equations using ADI-type integrators for parabolic problems. The instructor presents the origin of ADI-type integrators and explains the idea behind the trapezoidal rule. The lecture covers the stability function of AMF-W methods, classical order conditions, and time-independent boundary conditions. The instructor also outlines the talk, focusing on ADI-type integration methods from Rosenbrock to AMF-W methods, classical order conditions, and two main convergence theorems. The lecture concludes with an explanation of the recursion for the global error and three techniques for proving convergence.