Optimal stability for trapezoidal-backward difference split-steps
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 Ja...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Oxford University Press
2013
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| Online Access: | http://hdl.handle.net/1721.1/80879 https://orcid.org/0000-0001-7473-9287 |
| Summary: | 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. |
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