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 \(m\geq 2\). Numerical experiments will be presented to assess the PDE-convergence results.
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.
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.