W-Methods and Approximate Matrix Factorization for Parabolic PDEs with Mixed Derivative Terms

  1. González-Pinto, Severiano 1
  2. Hernández-Abreu, Domingo 1
  1. 1 Universidad de La Laguna
    info

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    ROR https://ror.org/01r9z8p25

Book:
Rosenbrock—Wanner–Type Methods

Publisher: Springer

ISSN: 2730-633X,  2730-6348

ISBN: 9783030768096,  9783030768102

Year of publication: 2021

Pages: 69-101

Type: Book chapter

DOI: 10.1007/978-3-030-76810-2_4 GOOGLE SCHOLAR lock_openOpen access editor

Sustainable development goals

Abstract

In this chapter W-methods are combined with the Approximate Matrix Factorization technique (AMF) in alternating direction implicit (ADI) sense for the time integration of parabolic partial differential equations with mixed derivatives in the elliptic operator, previously discretized in space by means of Finite Differences. Three different families of AMF-type W-methods are introduced and their unconditional stability is analized regardless of the spatial dimension. To this aim, a scalar test equation is presented and it is shown to be relevant for the class of problems under consideration when either periodic or homogeneous Dirichlet boundary conditions are imposed. Numerical results comparing the proposed AMF-type W-methods and some classical ADI schemes in the literature for 2 ≤ m ≤ 4 space dimensions are presented.

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