On the choice of correctors for semi-implicit Picard deferred correction methods

The goal of this study is to assess the implications of the choice of correctors for semi-implicit Picard integral deferred correction (SIPIDC) methods. The SIPIDC methods previously developed compute a high-order approximation by first computing a low-order provisional solution using a semi-implicit method and then using a first-order semi-implicit method to solve a series of correction equations, each of which raises the order of accuracy of the solution by one. In this study, we examine the efficiency of SIPIDC methods that instead use standard second-order semi-implicit methods to solve the correction equations. The accuracy, efficiency, and stability of the resulting methods are compared to previously developed methods, in the context of both nonstiff and stiff problems.