SEMI-IMPLICIT INTEGRAL DEFERRED CORRECTION CONSTRUCTED WITH ADDITIVE RUNGE-KUTTA METHODS

In this paper, we construct high order semi-implicit integrators using integral deferred correction (IDC) to solve stiff initial value problems. The general framework for the construction of these semi-implicit methods uses uniformly distributed nodes and additive Runge-Kutta (ARK) integrators as base schemes inside an IDC framework, which we refer to as IDC-ARK methods. We establish under mild assumptions that, when an r(th) order ARK method is used to predict and correct the numerical solution, the order of accuracy of the IDC method increases by r for each IDC prediction and correction loop. Numerical experiments support the established theorems, and also indicate that higher order IDC-ARK methods present an efficiency advantage over existing implicit-explicit (IMEX) ARK schemes in some cases.