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<p>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.</p>

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Interpolation preservation of AMF-W methods for linear diffusion problems

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年7月28日

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

摘要

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.