Adams methods for the efficient solution of stochastic differential equations with additive noise

Denk, Georg; Schäffler, Stefan

doi:10.1007/bf02684477

Cited by 31 publications

(17 citation statements)

References 9 publications

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“…However, in the inverse cascade regime where the nonlinear deterministic dynamics dominate the stochastic forcing, the numerical error is dominated by the deterministic part of the dynamics and a higher-accuracy treatment of the deterministic terms is justified. 27 The nondimensional width of the domain is in most cases L = 3, though in several cases it is reduced to L = 2 to allow increased resolution at fixed N. These values are large enough that the energy has room to spread outside the forcing region, yet small enough to be computationally tractable. The characteristic wavelength of the energy forcing should be less than the diameter of the forcing region, i.e., λ f = 2π/k f ≤ 1.…”

Section: -3 Ian Grooms Phys Fluids 27 101701 (2015)mentioning

confidence: 99%

A computational study of turbulent kinetic energy transport in barotropic turbulence on the f-plane

Grooms

2015

Physics of Fluids

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Energy transport by eddies is diagnosed from a series of simulations of stochastically forced, inhomogeneous two-dimensional turbulence—barotropic dynamics on the f-plane. The divergence of the energy flux is compared to diffusive models, both fractional and harmonic, and the inferred diffusivity κ is compared to a mixing-length model κ ∝ Vℓ where V and ℓ are eddy velocity and length scales, respectively. The flux-divergence is found to be well approximated by Laplacian diffusion with a mixing-length approximation. This study provides some support for diffusive modeling of mesoscale eddy energy transport in ocean model parameterizations.

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Section: -3 Ian Grooms Phys Fluids 27 101701 (2015)mentioning

confidence: 99%

A computational study of turbulent kinetic energy transport in barotropic turbulence on the f-plane

Grooms

2015

Physics of Fluids

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“…The situation is more complicated, however, once spontaneous emission is included. Equation (12) becomes (15) Even though both and are independent Gaussian processes, it is not entirely correct to replace the noise term on the right side with a single Gaussian noise process, because the optical phase is a dynamical variable stochastically perturbed by a noise term , which is correlated with the intensity noise.…”

Section: B Spontaneous Emission Noisementioning

confidence: 99%

“…Therefore, without loss of generality, we can define a new random variable , and this has exactly the same statistics as , namely , with each component being a random complex Gaussian as before. Thus, the explicit integration algorithm that we employ reads (20) In the simulation of some toy model problems (not shown), this algorithm produced results for the distribution of intensity that were the same as integrating the complex equation of motion, whereas integrating the equivalent of (15), assuming a single noise source on the intensity, gave incorrect answers.…”

Section: B Spontaneous Emission Noisementioning

confidence: 99%

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Synchronization and communication using semiconductor lasers with optoelectronic feedback

Abarbanel

Kennel

Illing

et al. 2001

IEEE J. Quantum Electron.

110

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Abstract-Semiconductor lasers provide an excellent opportunity for communication using chaotic waveforms. We discuss the characteristics and the synchronization of two semiconductor lasers with optoelectronic feedback. The systems exhibit broadband chaotic intensity oscillations whose dynamical dimension generally increases with the time delay in the feedback loop. We explore the robustness of this synchronization with parameter mismatch in the lasers, with mismatch in the optoelectronic feedback delay, and with the strength of the coupling between the systems. Synchronization is robust to mismatches between the intrinsic parameters of the lasers, but it is sensitive to mismatches of the time delay in the transmitter and receiver feedback loops. An open-loop receiver configuration is suggested, eliminating feedback delay mismatch issues. Communication strategies for arbitrary amplitude of modulation onto the chaotic signals are discussed, and the bit-error rate for one such scheme is evaluated as a function of noise in the optical channel.

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“…For β 2 = 0, the stochastic multi-step scheme (1.2) is explicit, otherwise it is drift-implicit. See also [3,4,7,8,9,13,14,17,18].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Mean-Square Stability of Two-Step Methods for Stochastic Ordinary Differential Equations

2006

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Abstract.We deal with linear multi-step methods for SDEs and study when the numerical approximation shares asymptotic properties in the mean-square sense of the exact solution.As in deterministic numerical analysis we use a linear time-invariant test equation and perform a linear stability analysis. Standard approaches used either to analyse deterministic multi-step methods or stochastic one-step methods do not carry over to stochastic multi-step schemes. In order to obtain sufficient conditions for asymptotic mean-square stability of stochastic linear two-step-Maruyama methods we construct and apply Lyapunov-type functionals. In particular we study the asymptotic meansquare stability of stochastic counterparts of two-step Adams-Bashforth-and AdamsMoulton-methods, the Milne-Simpson method and the BDF method.

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Adams methods for the efficient solution of stochastic differential equations with additive noise

Cited by 31 publications

References 9 publications

A computational study of turbulent kinetic energy transport in barotropic turbulence on the f-plane

A computational study of turbulent kinetic energy transport in barotropic turbulence on the f-plane

Synchronization and communication using semiconductor lasers with optoelectronic feedback

Asymptotic Mean-Square Stability of Two-Step Methods for Stochastic Ordinary Differential Equations

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