RT info:eu-repo/semantics/article
T1 A comparison of one-step and two-step W-methods and peer methods with approximate matrix factorization
A1 Hernández Abreu, Domingo
A1 Klinge, M.
A1 Weiner, R.
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 stability
K1 W-methods
K1 two-step W-methods
K1 peer methods
K1 convection-diffusion-reaction PDEs
AB One- and Two-step W-methods and peer methods are considered combined with an Approximate Matrix Factorization (AMF) for the numerical solution of large systems of stiff Ordinary Differential Equations (ODEs) coming from the spatial discretization of parabolic Partial Differential Equations (PDEs)of convection-diffusion-reaction type. Although one-step AMF W-methods do not require starting values and have larger stability regions, they may suffer from order reduction for such PDE problems when timedependent Dirichlet boundary conditions are imposed. Here by numerical tests it is illustrated that two-step AMF W-methods and AMF peer methods avoid this order reduction (in stiff sense, i.e. for a fixed spatial grid) due to their high stage order. On the other hand, while AMF W-methods are linearly implicit, AMFpeer methods require the solution of nonlinear equations in order to compute an advancing solution. In this case, the predictor considered for the internal stages influences both stability and accuracy. However, with only one Newton iteration, for a given number of stages, the three classes of methods have a similar computational cost.
YR 2019
FD 2019
LK http://riull.ull.es/xmlui/handle/915/39059
UL http://riull.ull.es/xmlui/handle/915/39059
LA en
DS Repositorio institucional de la Universidad de La Laguna
RD 21-nov-2024