RT info:eu-repo/semantics/article
T1 Higher-order exponential integrators for quasi-linear parabolic problems. Part II: Convergence
A1 González Fernández, Cesáreo Jesús
A1 Thalhammer, Mechthild
AB In this work, the convergence analysis of explicit exponential time integrators based on general linear methods for quasi-linear parabolic initial boundary value problems is pursued. Compared to other types of exponential integrators encountering rather severe order reductions, in general, the considered class of exponential general linear methods provides the possibility of constructing schemes that retain higher-order accuracy in time when applied to quasi-linear parabolic problems. In view of practical applications, the case of variable time step sizes is incorporated. The convergence analysis is based upon two fundamental ingredients. The needed stability bounds, obtained under mild restrictions on the ratios of subsequent time step sizes, have been deduced in the recent work [C. González and M. Thalhammer, SIAM J. Numer. Anal., 53 (2015), pp. 701--719]. The core of the present work is devoted to the derivation of suitable local and global error representations. In conjunction with the stability bounds, a convergence result is established.
SN 0036-1429
YR 2016
FD 2016
LK http://uvadoc.uva.es/handle/10324/28912
UL http://uvadoc.uva.es/handle/10324/28912
LA eng
NO SIAM Journal on Numerical Analysis 54-5 (2016), pp. 2868-2888
DS UVaDOC
RD 18-nov-2024