| Issue |
ESAIM: M2AN
Volume 50, Number 4, July-August 2016
|
|
|---|---|---|
| Page(s) | 1137 - 1166 | |
| DOI | https://doi.org/10.1051/m2an/2015072 | |
| Published online | 07 July 2016 | |
Error estimates of the integral deferred correction method for stiff problems∗
1 Department of Mathematics and Computer Science, University of
Catania, 95125 Catania, Italy.
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2 Department of Mathematics, University of Houston, 77004
Houston, USA.
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.
Received:
14
November
2014
Revised:
27
August
2015
Accepted:
28
August
2015
Abstract
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.
Mathematics Subject Classification: 65-XX
Key words: Stiff problems / Runge–Kutta methods / integral deferred correction methods / differential algebraic systems
Research supported by Air Force Office of Scientific Research YIP grant FA9550-12-0318, NSF grant DMS-1522777 and DMS-1217008 and University of Houston.
© EDP Sciences, SMAI 2016
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