Error estimates of the integral deferred correction method for stiff problems

Boscarino, Sebastiano; Qiu, Jing-Mei

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 1137-1166.

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 $\epsilon$. In our error estimates, we expand the global error in powers of $\epsilon$ 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.

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