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Divided and A-Divided Differences on Time Scales
, 2023 In this chapter, the divided differences and cr-divided differences on time scales are introduced. The Newton and cr-Newton interpolation polynomial are constructed. In addition, the Hermite interpolation polynomial on time scales is constructed by using
Erhan,I.M. +3 more
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Multiple time scale methods in tokamak magnetohydrodynamics [PDF]
, 1984 Several methods are discussed for integrating the magnetohydrodynamic (MHD) equations in tokamak systems on other than the fastest time scale. The dynamical grid method for simulating ideal MHD instabilities utilizes a natural nonorthogonal time-dependent coordinate transformation based on the magnetic field lines.
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Proper generalized decomposition of time-multiscale models [PDF]
, 2011 Models encountered in computational mechanics could involve many time scales. When these time scales cannot be separated, one must solve the evolution model in the entire time interval by using the finest time step that the model implies.
CHINESTA SORIA, Francisco +8 more
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Linear regulator design for stochastic systems by a multiple time scale method [PDF]
1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes, 1976 This short paper develops a hierarchically structured, suboptimal controller for a linear stochastic system composed of fast and slow subsystems. It is proved that the controller is optimal in the limit as the separation of time scales of the subsystems becomes infinite.
Teneketzis, Demosthenis +1 more
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International Journal for Computational Civil and Structural Engineering, 2020 Nonlinear force driven coupled vertical and torsional vibrations of suspension bridges, when the frequency of an external force is approaching one of the natural frequencies of the suspension system, which, in its turn, undergoes the conditions of the ...
Marina Shitikova, Aleks Katembo
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Near scale-free dynamics in neural population activity of waking/sleeping rats revealed by multiscale analysis. [PDF]
PLoS ONE, 2010 A neuron embedded in an intact brain, unlike an isolated neuron, participates in network activity at various spatial resolutions. Such multiple scale spatial dynamics is potentially reflected in multiple time scales of temporal dynamics. We identify such
Leonid A Safonov +5 more
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Lyapunov functions for linear nonautonomous dynamical equations on time scales [PDF]
, 2006 The existence of a Lyapunov function is established following a method of Yoshizawa for the uniform exponential asymptotic stability of the zero solution of a nonautonomous linear dynamical equation on a time scale with uniformly bounded ...
Peter E. Kloeden +3 more
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Geosensor Network Optimisation to Support Decisions at Multiple Scales
, 2023 Geosensor networks are often used to monitor processes at different spatial scales. Existing approaches for configuring geosensor locations (i.e. sample design) do not address two key challenges: 1) they are limited to a single scale of analysis and do ...
Comber, L, Harris, P.
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De La Vallée Poussin-type inequality for impulsive dynamic equations on time scales
, 2023 We derive a de La Vallée Poussin-type inequality for impulsive dynamic equations on time scales. This inequality is often used in conjunction with disconjugacy and/or (non)oscillation.
Özbekler,A. +3 more
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Computer algebra models dynamics on a multigrid across multiple length and time scales [PDF]
, 2007 [Abstract]: Methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time ...
Roberts, A. J.
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