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- W2911743140 abstract "Numerical evolution of time-dependent differential equations via explicit Runge-Kutta or Taylor methods typically fails to preserve symmetries of a system. It is known that there exists no numerical integration method that in general preserves both the energy and the symplectic structure of a Hamiltonian system. One is thus normally forced to make a choice. Nevertheless, a symmetric integration formula, obtained by Lanczos-Dyche via two-point Taylor expansion (or Hermite interpolation), is shown here to preserve both energy as well as symplectic structure for linear systems. This formula shares similarities with the Euler-Maclaurin formula, but is superconvergent rather than asymptotically convergent. For partial differential equations, the resulting evolution methods are unconditionally stable, i.e, not subject to a Courant-Friedrichs-Lewy limit. Although generally implicit, these methods become explicit for linear systems." @default.
- W2911743140 created "2019-02-21" @default.
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- W2911743140 date "2019-01-28" @default.
- W2911743140 modified "2023-09-27" @default.
- W2911743140 title "Time-symmetry, symplecticity and stability of Euler-Maclaurin and Lanczos-Dyche integration" @default.
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