Numerical Methods for Ordinary Differential Equations

Butcher, John

doi:10.1002/9781119121534

Cited by 1,088 publications

(626 citation statements)

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“…[20], there are many numerical examples demonstrating that the k-step scheme admits k-order convergence rate in solving FBSDEs, where k ≤ 6. However, when k > 6 the scheme becomes unstable, as classical numerical ODE theory predicts [3]. Our main purpose here is to provide a theoretical justification for such high-order convergence.…”

Section: Multistep Numerical Schemesmentioning

confidence: 98%

Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation

Yang¹,

Zhao²

2015

East Asian J. Appl. Math.

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Convergence analysis is presented for recently proposed multistep schemes, when applied to a special type of forward-backward stochastic differential equations (FB-SDEs) that arises in finance and stochastic control. The corresponding k-step scheme admits a k-order convergence rate in time, when the exact solution of the forward stochastic differential equation (SDE) is given. Our analysis assumes that the terminal conditions and the FBSDE coefficients are sufficiently regular.

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Section: Multistep Numerical Schemesmentioning

confidence: 98%

Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation

Yang¹,

Zhao²

2015

East Asian J. Appl. Math.

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“…Based on the topology snapshot interval η and the satellites initial positions

V_{0}

, the position matrix

V_{t} = {V_{t} | t = t_{0} + n η}

in the next snapshot can be calculated by using the satellite dynamic model and the Runge-Kutta algorithm [36]. Then, by repeating Step 1, the strategy obtains the topologies of the satellite cluster at every time of snapshot,

G_{t} = {G_{t} | t = t_{0} + n η}

.…”

Section: Reliability Assurance Topology Control Strategymentioning

confidence: 99%

A Topology Control Strategy with Reliability Assurance for Satellite Cluster Networks in Earth Observation

Chen

Zhang

2017

Sensors

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This article investigates the dynamic topology control problem of satellite cluster networks (SCNs) in Earth observation (EO) missions by applying a novel metric of stability for inter-satellite links (ISLs). The properties of the periodicity and predictability of satellites’ relative position are involved in the link cost metric which is to give a selection criterion for choosing the most reliable data routing paths. Also, a cooperative work model with reliability is proposed for the situation of emergency EO missions. Based on the link cost metric and the proposed reliability model, a reliability assurance topology control algorithm and its corresponding dynamic topology control (RAT) strategy are established to maximize the stability of data transmission in the SCNs. The SCNs scenario is tested through some numeric simulations of the topology stability of average topology lifetime and average packet loss rate. Simulation results show that the proposed reliable strategy applied in SCNs significantly improves the data transmission performance and prolongs the average topology lifetime.

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“…As the sampling period in this study (5 s) is short in relation to the speed of the system, Euler's implicit method [33] is …”

Section: A Discretization Of the Differential Equationsmentioning

confidence: 99%

A Variable Effective Capacity Model for <inline-formula> <tex-math notation="TeX">$\hbox{LiFePO}_{4}$</tex-math></inline-formula> Traction Batteries Using Computational Intelligence Techniques

Sánchez

Blanco

Anton

et al. 2015

IEEE Trans. Ind. Electron.

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Computational intelligence techniques are used to approximate the nonlinear operation of LiFePO 4 batteries using rule-based systems. In this paper, rulebased systems are not directly fitted to data, but comprise constructive blocks in a differential-equation-based dynamical model that is numerically integrated to infer battery voltage, charge, and temperature. The design methodology has been validated with three different LiFePO 4 batteries, and the results were found to be more accurate than those of a selection of statistical models and state-of-the-art artificial intelligence techniques. Index Terms-Computational intelligence, equivalent circuit model, LiFePO 4 batteries, semiphysical intelligent systems.0278-0046

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Numerical Methods for Ordinary Differential Equations

Cited by 1,088 publications

References 0 publications

Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation

Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation

A Topology Control Strategy with Reliability Assurance for Satellite Cluster Networks in Earth Observation

A Variable Effective Capacity Model for <inline-formula> <tex-math notation="TeX">$\hbox{LiFePO}_{4}$</tex-math></inline-formula> Traction Batteries Using Computational Intelligence Techniques

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