On PDE convergence of AMF-TASE W-methods for multidimensional linear parabolic problems

Domingo Hernández Abreu (Universidad de La Laguna), S. González Pinto, G. Rivero Herrera

This talk deals with the time-integration of space-discretised parabolic problems subject to Dirichlet boundary conditions on a rectangular m-dimensional domain. We consider a class of linearly implicit methods (TASE W-methods, [2]) in combination with Approximate Matrix Factorization [1] based on an alternating direction implicit approach, which allows to reduce the algebra cost to the level of one-dimensional problems. Optimal results on PDE-convergence will be presented for linear problems, the Euclidean norm and arbitrary spatial dimensions m≥2. Numerical experiments will be presented to assess the PDE-convergence results.

References

  1. D. Conte, S. González-Pinto, D. Hernández-Abreu and G. Pagano. On Approximate Matrix Factorization and TASE W-methods for the time integration of parabolic Partial Differential Equations. J. Sci. Comput. 100(2), 34, 2024.

  2. S. González-Pinto, D. Hernández-Abreu, G. Pagano and S. Pérez-Rodrı́guez. Generalized TASE-RK methods for stiff problems. Appl. Numer. Math. 188, 129-145, 2023.

[link to pdf] [back to Numdiff-17]