---

Interpolation preservation of AMF-W methods for linear diffusion problems

---

Severiano González-Pinto, Ernst Hairer, and Domingo Hernández-Abreu,

---

Abstract. This article considers the numerical integration of linear diffusion problems in high space dimension by AMF-W methods. These are methods of the type ADI (alternating direction implicit). We focus on the treatment of general Dirichlet boundary conditions. New is the introduction of a property -- interpolation preservation -- which permits to extend convergence results for homogeneous boundary conditions to general time-dependent boundary conditions. Numerical experiments confirm the theoretical results.

---

Key Words. Parabolic partial differential equations, AMF-W methods, interpolation preservation, PDE-convergence, time-dependent Dirichlet boundary conditions.

---