Semi-implicit Krylov Deferred Correction Methods for Differential Algebraic Equations

Abstract: In the recently developed Krylov deferred correction (KDC) methods for ordinary differential equation initial value problems [11], a Picard-type collocation formulation is preconditioned using low-order time integra-tion schemes based on spectral deferred correction (SDC), and the resulting system is solved efficiently using a Newton-Krylov method. Existing analyses show that these KDC methods are super convergent, A-stable, B-stable, symplectic, and symmetric. In this paper, we investigate the efficiency of semi-implicit KDC (SI-KDC) methods for problems which can be decomposed into stiff and non-stiff components. Preliminary analysis and numerical results show that SI-KDC methods display very similar convergence of Newton-Krylov iterations compared with fully-implicit (FI-KDC) methods but can significantly reduce the computational cost in each SDC iteration for the same accuracy requirement for certain problems