RT info:eu-repo/semantics/article
T1 Avoiding order reduction phenomenon for general linear methods when integrating linear problems with time dependent boundary values
A1 Alonso Mallo, Isaías
A1 Reguera López, Nuria
K1 Order reduction
K1 General linear methods
K1 Initial boundary value problems
K1 Matemáticas
K1 Mathematics
AB When applied to stiff problems, the effective order of convergence of general linear methods is governed by their stage order, which is less than or equal to the classical order of the method. This produces an order reduction phenomenon, present in all general linear methods except those with high stage order, in a manner similar to that observed in other time integrators with internal stages. In this paper, we investigate the order reduction which arises when general linear methods are used as time integrators when using the method of lines for solving numerically initial boundary value problems with time dependent boundary values. We propose a technique, based on making an appropriate choice of the boundary values for the internal stages, with which it is possible to recover one unit of order, as weprove in this work. As expected, this implies a considerable improvement for the general linear methods suffering order reduction. Moreover, numerical experiments show that the improvement is not only in these cases, but that, even when the order reduction is not expected, the size of the errors is drastically reduced by using the technique proposed in this paper.
PB Elsevier
SN 0377-0427
YR 2024
FD 2024-03
LK http://hdl.handle.net/10259/7969
UL http://hdl.handle.net/10259/7969
LA eng
NO This research has been supported by project PGC2018-101443-B-100, Ministerio de Ciencia, Innovación y Universidades (Spain) and by Junta de Castilla y León (Grant numbers VA169P20 and VA193P20).
DS Repositorio Institucional de la Universidad de Burgos
RD 22-dic-2024