RT info:eu-repo/semantics/article
T1 On Approximate Matrix Factorization and TASE W-Methods for the Time Integration of Parabolic Partial Differential Equations
A1 Hernández Abreu, Domingo
A1 Conte, Dajana
A1 González Pinto, Severiano
A1 Pagano, Giovanni
A2 Análisis Matemático
A2 Grupo de investigación ULL:
"Métodos numéricos en ecuaciones diferenciales"
https://www.ull.es/grupoinvestigacion/met-numericos-ec-diferenciales/
K1 Approximate Matrix Factorization
K1 TASE W-methods
K1 consistency
K1 time integration
K1 parabolic PDEs
AB Linearly implicit methods for Ordinary Differential Equations combined with theapplication of Approximate Matrix Factorization (AMF) provide efficient numerical methods for the solution of large semi-discrete parabolic Partial DifferentialEquations in several spatial dimensions. Interesting particular subclasses of suchlinearly implicit methods are the so-called W-methods and the TASE W-methods recently introduced in [11] with the aim of reducing the computational cost of the TASE Runge-Kutta methods in [1] and [4]. In this paper, we study the application of the AMF approach in combination with TASE W-methods. While forAMF W-methods the temporal order of consistency is immediately obtained fromthat of the underlying W-method, this property needs a more thorough analysisfor the newly introduced AMF-TASE W-methods. For these latter methods it isdescribed which are the additional order conditions to be fulfilled and it is shownthat the parallel structure of the methods is crucial to retain the order of consistency of the underlying TASE W-method. Numerical experiments are presented in three spatial dimensions to assess the consistency result and to show that the proposed schemes are competitive with other well-known good performing AMF W-methods.
YR 2024
FD 2024
LK http://riull.ull.es/xmlui/handle/915/39043
UL http://riull.ull.es/xmlui/handle/915/39043
LA en
DS Repositorio institucional de la Universidad de La Laguna
RD 24-nov-2024