Geodesic
Error estimates of the integral deferred correction method for stiff problems
Boscarino, Sebastiano1 ; Qiu, Jing-Mei2
1 Department of Mathematics and Computer Science, University of Catania, 95125 Catania, Italy.
2 Department of Mathematics, University of Houston, 77004 Houston, USA.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 1137-1166

Voir la notice de l'article provenant de la source Numdam

In this paper, we present error estimates of the integral deferred correction method constructed with stiffly accurate implicit Runge–Kutta methods with a nonsingular matrix A in its Butcher table representation, when applied to stiff problems characterized by a small positive parameter ε. In our error estimates, we expand the global error in powers of ε and show that the coefficients are global errors of the integral deferred correction method applied to a sequence of differential algebraic systems. A study of these errors and of the remainder of the expansion yields sharp error bounds for the stiff problem. Numerical results for the van der Pol equation are presented to illustrate our theoretical findings. Finally, we study the linear stability properties of these methods.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2015072
Classification : 65-XX
Keywords: Stiff problems, Runge–Kutta methods, integral deferred correction methods, differential algebraic systems

Boscarino, Sebastiano 1 ; Qiu, Jing-Mei 2

1 Department of Mathematics and Computer Science, University of Catania, 95125 Catania, Italy.
2 Department of Mathematics, University of Houston, 77004 Houston, USA. 
@article{M2AN_2016__50_4_1137_0,
     author = {Boscarino, Sebastiano and Qiu, Jing-Mei},
     title = {Error estimates of the integral deferred correction method for stiff problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1137--1166},
     publisher = {EDP-Sciences},
     volume = {50},
     number = {4},
     year = {2016},
     doi = {10.1051/m2an/2015072},
     zbl = {1364.65151},
     mrnumber = {3521715},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015072/}
}
TY  - JOUR
AU  - Boscarino, Sebastiano
AU  - Qiu, Jing-Mei
TI  - Error estimates of the integral deferred correction method for stiff problems
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2016
SP  - 1137
EP  - 1166
VL  - 50
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015072/
DO  - 10.1051/m2an/2015072
LA  - en
ID  - M2AN_2016__50_4_1137_0
ER  - 
%0 Journal Article
%A Boscarino, Sebastiano
%A Qiu, Jing-Mei
%T Error estimates of the integral deferred correction method for stiff problems
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2016
%P 1137-1166
%V 50
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015072/
%R 10.1051/m2an/2015072
%G en
%F M2AN_2016__50_4_1137_0
Boscarino, Sebastiano; Qiu, Jing-Mei. Error estimates of the integral deferred correction method for stiff problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 1137-1166. doi: 10.1051/m2an/2015072

Cité par Sources :