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Decoupling Abstractions of Non-linear Ordinary Differential Equations
[chapter]

2016
*
Lecture Notes in Computer Science
*

HAL is a multi-disciplinary open access archive for the deposit and dissemination

doi:10.1007/978-3-319-48989-6_38
fatcat:6nsv4hajczfoxgatzt7j63x4be
*of*scientific research documents, whether they are published or not. ... L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou*non*, émanant des établissements d'enseignement et de recherche ... André Platzer at Carnegie Mellon University for his technical questions and helpful insights into*differential*ghosts. Bibliography ...##
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Page 3965 of Mathematical Reviews Vol. , Issue 87g
[page]

1987
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Mathematical Reviews
*

A finite-dimensionality property is added and the au- thor points out that he obtains an

*abstract*formulation*of*the system described by the standard*ordinary**differential**equation*z= Az+Br, y= z+Dcz. ... Akhundov, A survey*of*certain results in the the- ory*of**linear**differential**equations*that are unsolved with respect to the derivative (Russian) (pp. 7-16); J. ...##
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Explicit triangular decoupling of the separated vector wave equation on Schwarzschild into scalar Regge-Wheeler equations

2018
*
Journal of Physics, Conference Series
*

After a separation

doi:10.1088/1742-6596/968/1/012006
fatcat:3ms2cmm6xbadfjpfofupd7inwe
*of*variables, the radial mode*equations*form a complicated system*of*coupled*linear*ODEs. ... We outline a precise*abstract*strategy to*decouple*this system into triangular form, where the diagonal blocks consist*of*spin-s scalar Regge-Wheeler*equations*, with s=0 or 1. ... The author also thanks Francesco Bussola for checking some*of*this paper's calculations as part*of*his MSc thesis [14] . ...##
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Analytical and Numerical Methods for Solving Partial Differential Equations and Integral Equations Arising in Physical Models

2014
*
Abstract and Applied Analysis
*

Mathematical modelling

doi:10.1155/2014/635235
fatcat:qbbhlyakrzhq5cur6x6wnztzqu
*of*real-life problems usually results in functional*equations*, like*ordinary*or partial*differential**equations*, integral and integrodifferential*equations*, and stochastic*equations*... One*of*the papers is*of*use*of*Sumudu transform on fractional derivatives for solving some interesting nonhomogeneous fractional*ordinary**differential**equations*. ... Mathematical modelling*of*real-life problems usually results in functional*equations*, like*ordinary*or partial*differential**equations*, integral and integrodifferential*equations*, and stochastic*equations*...##
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Page 5516 of Mathematical Reviews Vol. , Issue 2000h
[page]

2000
*
Mathematical Reviews
*

The approaches are based on the reduction

*of*inverse problems to boundary value problems for finite or infinite systems*of**non*-*linear**equations*. ... In*abstract*formulation, using the compact resolvent*of*a Fredholm operator the authors apply the general global Hopf bifurcation theorem for neutral*ordinary**equations*. ...##
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Adaptive partitioning techniques for ordinary differential equations

2006
*
BIT Numerical Mathematics
*

Many stiff systems

doi:10.1007/s10543-006-0074-z
fatcat:rxzvf6kjifaqjiw6hnanxcucle
*of**ordinary**differential**equations*(ODEs) modeling practical problems can be partitioned into loosely coupled subsystems. ... In memory*of*Germund Dahlquist (1925Dahlquist ( -2005.*Abstract*. ... The numerical solution*of*a stiff system*of*S*ordinary**differential**equations*(ODEs) may have computational complexity up to O(S 3 ) because*of*the*linear*algebra. ...##
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Page 1946 of Mathematical Reviews Vol. , Issue 93d
[page]

1993
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Mathematical Reviews
*

Summary (translated from the Russian): “We develop an algorithm for the asymptotic splitting

*of*a*linear*homogeneous singularly per- turbed system*of**ordinary**differential**equations*with a degenerate limit ... after which we continue the solution to the en- tire interval*of*change*of*the independent variable considered by the method*of*‘matching’*of*asymptotic solutions.” 34*ORDINARY**DIFFERENTIAL**EQUATIONS*34F ...##
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Page 3662 of Mathematical Reviews Vol. , Issue 98F
[page]

1998
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Mathematical Reviews
*

It is now well-known that a straightforward set-valued generalization

*of*the Euler scheme works just as well in the multivalued case*of*control systems as it does with*ordinary**differential**equations*. ... Time discretization is fundamental to the theory*of**ordinary*dif- ferential*equations*. ...##
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Page 7 of Mathematical Reviews Vol. , Issue 2001A
[page]

2001
*
Mathematical Reviews
*

Vath,

*Linear*and nonlinear*abstract*Volterra*equations*(499-512); H.-O. Walther, The singu- larities*of*an attractor*of*a delay*differential**equation*(513-548). ... Reinfelds, Partial*decoupling**of*noninvertible impulsive*differential**equations*(425-438); H. G. Rotstein, A. I. Domosh- nitsky and A. A. ...##
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Coupling vs decoupling approaches for PDE/ODE systems modeling intercellular signaling

2016
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Journal of Computational Physics
*

For biologically relevant configurations

doi:10.1016/j.jcp.2016.03.020
fatcat:se5f6laurrbdxa7splxx74y2j4
*of*the model, our quantitative study shows that a coupling approach performs much better than a*decoupling*one. ... Based on a sensitivity analysis, we present a systematic comparison between coupling and*decoupling*approaches for this class*of*problems and show numerical results. ... Rolf Rannacher for the numerous fruitful discussions on numerical aspects*of*this work. Furthermore, the authors acknowledge Prof. ...##
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Page 6183 of Mathematical Reviews Vol. , Issue 88k
[page]

1988
*
Mathematical Reviews
*

The plant could be described, for example, by a system

*of**ordinary*or partial*differential**equations*or an integral*equation*. ... All that is required is that its input-output properties be described by a*linear*or*non*-*linear*operator. The control system is described by a system*of*difference*equations*. ...##
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Linear and quasi-linear iterative splitting methods: Theory and applications

2007
*
International Mathematical Forum
*

The stability analysis is based on the A-stability

doi:10.12988/imf.2007.07212
fatcat:kvpxt6y2kvckpgbligxnd6zm7i
*of**ordinary**differential**equations*, and the importance*of*including weighted parameters for relaxing the iterative operator-splitting methods can be seen ... The exactness and the efficiency*of*the methods are investigated through solutions*of*nonlinear model problems*of*parabolic*differential**equations*, for example systems*of*convection-reaction-diffusion ... The discretization*of*the*linear**ordinary**differential**equation*is done with the BDF3 method. Our numerical results are presented in table 5.2. ...##
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Tuning Strategies for Online-Adaptive PI Controllers

2007
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Oil & Gas Science and Technology
*

The closed-loop air path poles are calculated online through a

doi:10.2516/ogst:2007045
fatcat:6zbt63ppynfrle7ahrcgr5zegy
*linearized*parameter variable thermodynamic process model (LPV model). ... This routine is based on the placement*of*the closed-loop air path poles. ... This block diagram can be derived from*non*-*linear**ordinary**differential**equations*describing the thermodynamic and mechanical behaviour*of*the air path. ...##
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Page 1371 of Mathematical Reviews Vol. 54, Issue 4
[page]

1977
*
Mathematical Reviews
*

*Ordinary*

*differential*

*equations*(Proc. Conf., Math. Res. Center, Naval Res. Lab., Washington, D.C., 1971), pp. 459-471. Academic Press, New York, 1972. ... Kréevinac (Belgrade) Singh, Sudarshan Pal; Liu, Ruey Wen 9742 Existence

*of*state

*equation*representation

*of*

*linear*large-scale dynamical systems. Large-scale networks. IEEE Trans. ...

##
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Splitting schemes for the semi-linear wave equation with dynamic boundary conditions
[article]

2021
*
arXiv
*
pre-print

This paper introduces novel splitting schemes

arXiv:2112.04321v1
fatcat:7ikz6snyxzhnhnhk5l54lgfkre
*of*first and second order for the wave*equation*with kinetic and acoustic boundary conditions*of*semi-*linear*type. ... For kinetic boundary conditions, we propose a reinterpretation*of*the system*equations*as a coupled system. ... Note that (4.1) is an*ordinary**differential**equation*such that no regularization as for kinetic boundary conditions is necessary. ...
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