Semi-implicit Krylov deferred correction methods for ordinary differential equations

Authors:
Sunyoung Bu;Jingfang Huang;Michael L. Minion
Affiliations:
University of North Carolina, Department of Mathematics, Chapel Hill;University of North Carolina, Department of Mathematics, Chapel Hill;University of North Carolina, Department of Mathematics, Chapel Hill
Venue:
AMATH'09 Proceedings of the 15th american conference on Applied mathematics
Year:
2009

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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 integration 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.