Precisely A(alpha)-stable one-leg multistep methods
(2003) Bit (Lisse) : numerical mathematics — Vol. 43, n° 4, p. 761-774 (2003)
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- One-Leg Multistep (OLM) methods for initial value problems in ODEs use a nonlinear multistep formula to compute the solution at the next integration point. This paper shows that there exists an evaluation point t* which gives an OLM formula more precise than BDF's and (almost) precisely A(alpha)-stable for a k-step method (k less than or equal to 6), and whose stability angle is essentially similar to BDF's. The stability region can be further improved by applying the corrector idea of Klopfenstein.
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Janssen, M., & Van Hentenryck, P. (2003). Precisely A(alpha)-stable one-leg multistep methods. Bit (Lisse) : numerical mathematics, 43(4), 761-774. https://doi.org/10.1023/B:BITN.0000009944.34359.79 (Original work published 2003)