NDLI: Semi-implicit Krylov deferred correction methods for ordinary differential equations

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Semi-implicit Krylov deferred correction methods for ordinary differential equations

Content Provider	Semantic Scholar
Author	Bu, Sunyoung Huang, Jingfang Minion, Michael L.
Copyright Year	2009
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.
Starting Page	95
Ending Page	100
Page Count	6
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://people.cs.vt.edu/~asandu/Public/For/Michael/Minion_2009_semi-implicit.pdf
Alternate Webpage(s)	http://www.wseas.us/e-library/conferences/2009/houston/AAMCIS1/AAMCIS1-15.pdf
Alternate Webpage(s)	http://www.amath.unc.edu/Faculty/minion/pubs/PDF/SIKDC-WSEAS.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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