Optimal stability for trapezoidal-backward difference split-steps
Name
Strang_Optimal stability.pdf
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49.69 KB
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Adobe PDF
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Author(s)
Dharmaraja, Sohan
Wang, Yinghui
Strang, Gilbert
Date Issued
September 2009
Journal
IMA Journal of Numerical Analysis
Publisher
Oxford University Press
Citation
Dharmaraja, S., Y. Wang, and G. Strang. “Optimal stability for trapezoidal-backward difference split-steps.” IMA Journal of Numerical Analysis 30, no. 1 (January 21, 2010): 141-148.
Version
Author's final manuscript
Abstract
The marginal stability of the trapezoidal method makes it dangerous to use for highly non-linear oscillations. Damping is provided by backward differences. The split-step combination (αΔt trapezoidal, (1 – α)Δt for BDF2) retains second-order accuracy. The ‘magic choice’ a = 2 – √2 allows the same Jacobian for both steps, when Newton's method solves these implicit difference equations. That choice is known to give the smallest error constant, and we prove that a = 2 – √2 also gives the largest region of linearized stability.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1093/imanum/drp022
