2009 PIMS-CSC Seminar - 01

A class of novel deferred correction methods, integral deferred correction (IDC) methods [2], is studied. This class of methods is an extension of ideas introduced by Dutt, Greengard and Rokhlin [1] on spectral deferred correction (SDC) methods for solving ODEs. The novel nature of this class of methods, is that the correction of the defect is carried out using an accurate integral form of the residual instead of the more familiar differential form. As a family of methods, these schemes are capable of matching the efficiency of popular high order RK methods [3]. Additionally, the regions of absolute stability of such IDC schemes are vastly superior. The application problems of interest are the behavior of plasmas in the presence of electromagnetic fields.

[1] Dutt, Greengard and Rokhlin, Spectral deferred correction methods for ODEs, BIT, 40 (2000), pp. 241-266

[2] Christlieb, Ong, Qiu, "Spectral" deferred correction methods constructed with high order Runge-Kutta integrators, Math. Comp, accepted

[3] Christlieb, Ong, Qiu, Comments on high order integrators embedded within integral deferred correction methods, Appl. Num. Math., accepted