Stability and Convergence of the Peaceman-Rachford ADI (Alternating Direction Implicit) Method for Initial-Boundary Value Problems

摘要

The alternating direction implicit method of Peaceman and Rachford applied to initial-boundary value problems for partial differential equations in two space dimensions is analyzed using the method of lines approach. Motivated by developments in the field of stiff nonlinear ordinary differential equations, the analysis focuses on problems where the semidiscrete system, obtained after discretization in space, satisfies a one sided Lipschitz condition with a constant independent of the grid spacing. For such problems, unconditional stability and convergence results are derived.