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 Reguera, N.
A1 Alonso Mallo, Isaías
K1 Matemáticas
K1 Algebra lineal
K1 Order reduction
K1 General linear methods
K1 Initial boundary value problems
K1 Reducción de pedido
K1 Métodos lineales generales
K1 Problemas de valores límite iniciales
K1 12 Matemáticas
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 we prove 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
LK https://uvadoc.uva.es/handle/10324/62691
UL https://uvadoc.uva.es/handle/10324/62691
LA eng
NO Journal of Computational and Applied Mathematics, 2024, vol. 439, 115629
NO Producción Científica
DS UVaDOC
RD 18-nov-2024