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

Andrew Sogokon, Khalil Ghorbal, Taylor T. Johnson
2016 Lecture Notes in Computer Science  
HAL is a multi-disciplinary open access archive for the deposit and dissemination 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  ... 
doi:10.1007/978-3-319-48989-6_38 fatcat:6nsv4hajczfoxgatzt7j63x4be

Page 3965 of Mathematical Reviews Vol. , Issue 87g [page]

1987 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.  ... 

Explicit triangular decoupling of the separated vector wave equation on Schwarzschild into scalar Regge-Wheeler equations

Igor Khavkine
2018 Journal of Physics, Conference Series  
After a separation 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] .  ... 
doi:10.1088/1742-6596/968/1/012006 fatcat:3ms2cmm6xbadfjpfofupd7inwe

Analytical and Numerical Methods for Solving Partial Differential Equations and Integral Equations Arising in Physical Models

Santanu Saha Ray, Om P. Agrawal, R. K. Bera, Shantanu Das, T. Raja Sekhar
2014 Abstract and Applied Analysis  
Mathematical modelling 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  ... 
doi:10.1155/2014/635235 fatcat:qbbhlyakrzhq5cur6x6wnztzqu

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.  ... 

Adaptive partitioning techniques for ordinary differential equations

Stig Skelboe
2006 BIT Numerical Mathematics  
Many stiff systems 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.  ... 
doi:10.1007/s10543-006-0074-z fatcat:rxzvf6kjifaqjiw6hnanxcucle

Page 1946 of Mathematical Reviews Vol. , Issue 93d [page]

1993 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  ... 

Page 3662 of Mathematical Reviews Vol. , Issue 98F [page]

1998 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.  ... 

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.  ... 

Coupling vs decoupling approaches for PDE/ODE systems modeling intercellular signaling

Thomas Carraro, Elfriede Friedmann, Daniel Gerecht
2016 Journal of Computational Physics  
For biologically relevant configurations 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.  ... 
doi:10.1016/ fatcat:se5f6laurrbdxa7splxx74y2j4

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.  ... 

Linear and quasi-linear iterative splitting methods: Theory and applications

J. Geiser
2007 International Mathematical Forum  
The stability analysis is based on the A-stability 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.  ... 
doi:10.12988/imf.2007.07212 fatcat:kvpxt6y2kvckpgbligxnd6zm7i

Tuning Strategies for Online-Adaptive PI Controllers

L. Däubler, C. Bessai, O. Predelli
2007 Oil & Gas Science and Technology  
The closed-loop air path poles are calculated online through a 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.  ... 
doi:10.2516/ogst:2007045 fatcat:6zbt63ppynfrle7ahrcgr5zegy

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.  ... 

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

Robert Altmann
2021 arXiv   pre-print
This paper introduces novel splitting schemes 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.  ... 
arXiv:2112.04321v1 fatcat:7ikz6snyxzhnhnhk5l54lgfkre
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