AMF-type W-methods for the time integration of parabolic PDEs with mixed derivative terms (Domingo Hernández-Abreu, University of La Laguna)

11.06.2018 14:00

This talk deals with W-methods [4] in combination with the Approximate Matrix Factorization technique (AMF) in alternating direction implicit (ADI) sense for the time integration of parabolic partial differential equations with mixed derivative terms in the elliptic operator, previously discretized in space by means of Finite Differences [3].

Three different families of AMF-type W-methods are presented and their unconditional stability is studied regardless of the spatial dimension. To this aim, a scalar test equation is introduced and shown to be relevant for the class of problems under consideration when either periodic or homogeneous Dirichlet boundary conditions are imposed.

The proposed AMF-type W-methods and some classical ADI schemes in the literature are compared through numerical experiments with a linear parabolic problem in dimension m = 3 and m = 4 and with the Heston problem from financial option pricing.

This work is done in collaboration with Severiano González-Pinto, Ernst Hairer and Soledad-Pérez Rodríguez [1, 2].

References
[1] S. González-Pinto, E. Hairer, D. Hernández-Abreu and S. Pérez-Rodríguez. AMF-type W-methods for parabolic PDEs with mixed derivatives. Submitted for publication.
[2] S. González-Pinto, E. Hairer, D. Hernández-Abreu and S. Pérez-Rodríguez. PDE-W-methods for parabolic problems with mixed derivatives. To appear in Numer. Algor.
[3] W. Hundsdorfer and J.G. Verwer. Numerical solution of time-dependent advection-diffusion-reaction equations. Springer-Verlag, Berlin, 2003.
[4] T. Steihaug and A. Wolfbrandt. An attempt to avoid exact Jacobian and nonlinear equations in the numerical solution of stiff differential equations. Math. Comp., 33(146):521–534, 1979.

Lieu

salle 623, Séminaire d'analyse numérique

entrée libre