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 in its Butcher table representation, when applied to stiff problems characterized by a small positive parameter . In our error estimates, we expand the global error in powers of 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.
Accepted:
DOI: 10.1051/m2an/2015072
Keywords: Stiff problems, Runge–Kutta methods, integral deferred correction methods, differential algebraic systems
@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://www.numdam.org/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://www.numdam.org/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://www.numdam.org/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 , Volume 50 (2016) no. 4, pp. 1137-1166. doi : 10.1051/m2an/2015072. http://www.numdam.org/articles/10.1051/m2an/2015072/
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