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Linear Complete Differential Resultants and the Implicitization of Linear DPPEs
[article]

2008
*
arXiv
*
pre-print

We study the computation by

arXiv:0712.0785v2
fatcat:2dbtj6vwunbqversab5vhf2j3i
*linear*complete*differential**resultants*of the*implicit*equation of a system of n*linear**differential*polynomial parametric equations in n-1*differential*parameters. ... The*linear*complete*differential**resultant*of a finite set of*linear*ordinary*differential*polynomials is defined. ...*Implicitization*of*linear*DPPEs by*linear*Complete*Differential**Resultants*Let P(X, U), F i , H i be as in Section 2*and*let ID be the*implicit*ideal of P(X, U). ...##
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Linear complete differential resultants and the implicitization of linear DPPEs

2010
*
Journal of symbolic computation
*

We study the computation by

doi:10.1016/j.jsc.2009.09.003
fatcat:ltyyzb2e5nalhhxd3uc7fhigry
*linear*complete*differential**resultants*of the*implicit*equation of a system of n*linear**differential*polynomial parametric equations in n − 1*differential*parameters. ... The*linear*complete*differential**resultant*of a finite set of*linear*ordinary*differential*polynomials is defined. ... Acknowledgements The authors thank the referees for their questions*and*comments allowing the achievement of the final version of this paper. ...##
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An A- Stable Block Integrator Scheme for the Solution of First Order System of IVP of Ordinary Differential Equations

2022
*
Asian Journal of Probability and Statistics
*

Some test problems are solved with the proposed scheme

doi:10.9734/ajpas/2022/v16i430407
fatcat:k5b7n4ywr5gy7o2vy2dkspxjqi
*and*the*result*are compared with some existing method. ... Hence, the method is recommended for solving first order system of IVP of ordinary*differential*equations. ... Definition 6 (Explicit*and**Implicit*method) The general*linear*multi-step method is said to be Explicit if , otherwise it is*Implicit*. ...##
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A perturbed differential resultant based implicitization algorithm for linear DPPEs
[article]

2010
*
arXiv
*
pre-print

A nonzero

arXiv:1003.4375v1
fatcat:a3cmwxduo5dgtcj27eg4h6q45m
*linear**differential*polynomial in 𝕀 is obtained from the lowest degree term of _ϕ*and*used to provide an*implicitization*algorithm for . ... We prove the existence of a*linear*perturbation _ϕ of so that the*linear*complete*differential**resultant*_ϕ associated to _ϕ is nonzero. ... Rafael Sendra for kindly reading*and*commenting on some parts of this work. ...##
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A perturbed differential resultant based implicitization algorithm for linear DPPEs

2011
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Journal of symbolic computation
*

A nonzero

doi:10.1016/j.jsc.2011.05.001
fatcat:yqcxqqz2gneu7ls2u4za7jaoiy
*linear**differential*polynomial in ID is obtained, from the lowest degree term of ∂CRes φ ,*and*used to provide an*implicitization*for P . ... We prove the existence of a*linear*perturbation P φ of P , so that the*linear*complete*differential**resultant*∂CRes φ associated to P φ is nonzero. ... DPPEs,*and*use*linear*complete*differential**resultants*to give a candidate for the*implicit*equation of the system. ...##
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Page 6923 of Mathematical Reviews Vol. , Issue 95k
[page]

1995
*
Mathematical Reviews
*

Both negative

*and*positive*results*are presented. ... These*results*can be used as an explanation for possible causes*and*cures of slow convergence*and*nonconvergence of steady-state numerical solutions when using an*implicit*LMM time-dependent approach in ...##
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Page 3740 of Mathematical Reviews Vol. , Issue 2003e
[page]

2003
*
Mathematical Reviews
*

As a

*result*, we produce a new efficient procedure to solve*linear*systems arising in an application of*implicit*Runge-Kutta methods to large-scale*differential*-algebraic equations of index 1. ...*Linear**and*non-*linear*illustrations are given to show the practical usefulness of the approach developed. ...##
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Transactions of the chemical engineering congress

2010
*
Journal of the Society of Chemical Industry
*

This ODE involves a reduced number of dependent variables,

doi:10.1002/jctb.5000562803
fatcat:ytn7bwlfv5cchit5zmm2v3ftue
*and*some evaluations of*implicit*functions defined, either from the original algebraic constraints, or from the hidden ones. ... After two deflation steps, this DAE is converted to an equivalent first-order explicit ordinary*differential*equation (ODE). ... For such a quasi*linear*DAE model, the*differentiation*index is more difficult to define,*and*to compute, than in the*linear*case. ...##
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Converting DAE Models to ODE Models: Application to Reactive Rayleigh Distillation

2013
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Chemical Engineering Transactions
*

This ODE involves a reduced number of dependent variables,

doi:10.3303/cet1332220
doaj:a5fe247b60374415bfb6f0fbef8bb65b
fatcat:lptnkwt2ufcunfgssf4qiepnja
*and*some evaluations of*implicit*functions defined, either from the original algebraic constraints, or from the hidden ones. ... After two deflation steps, this DAE is converted to an equivalent first-order explicit ordinary*differential*equation (ODE). ... For such a quasi*linear*DAE model, the*differentiation*index is more difficult to define,*and*to compute, than in the*linear*case. ...##
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Page 3194 of Mathematical Reviews Vol. , Issue 86g
[page]

1986
*
Mathematical Reviews
*

For the

*linear*autonomous system y’ = Ay, these linearly*implicit*methods are identical with certain*implicit*multistep*and*one-leg methods, respectively. ... For the stiff equations*implicit*backward*differentiation*formulae are used*and*for the remaining equations Adams formulae with a variable-order code are used. ...##
###
Page 3596 of Mathematical Reviews Vol. , Issue 95f
[page]

1995
*
Mathematical Reviews
*

wave speed

*and*a time constant, from the*resulting*al- gebraic eigenvalue problem. ... ’ of these iterative*implicit*schemes are revealed*and*compared. ...##
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Linearization methods for reaction-diffusion equations: 1-D problems

1997
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Applied Mathematics and Computation
*

The second one requires the solution of two-point,

doi:10.1016/s0096-3003(96)00328-1
fatcat:ikz4iqwdlzcbzgdzqjkg3ydvty
*linear*, ordinary*differential*equations*and*provides either piecewise continuous or piecewise*differentiable*solutions in space*and*discrete in time. ... The third type is based on the discretization of the spatial coordinate*and*provides a system of*linear*, ordinary*differential*equations in time which can be integrated analytically. ... Garc'za-Lbpez for some useful comments on the relation between Rosenbrock's methods*and**linearized*O-methods. ...##
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Page 5317 of Mathematical Reviews Vol. , Issue 2004g
[page]

2004
*
Mathematical Reviews
*

*Differential*Equations 19 (2003), no. 2, 170-181. In this paper the author states

*and*proves a

*result*of Jorba-Simo type [A. Jorba

*and*C. Simo, J. ... Although there have been a number of articles that approach

*implicit*

*differential*equa- tions algebraically, all such approaches have relied heavily on

*linear*algebra. ...

##
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Page 5101 of Mathematical Reviews Vol. , Issue 92i
[page]

1992
*
Mathematical Reviews
*

Ordinary

*differential*equations 92i:65118 ods (for example, explicit*and**implicit*Runge-Kutta methods) is discussed. ... Other topics treated are the following: the computational complexity involved in*implicit*or semi-*implicit*methods*and*in local error estimation for explicit methods;*linear*stability theory examined as ...##
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Linear-implicit strong schemes for Itô-Galkerin approximations of stochastic PDEs

2001
*
Journal of Applied Mathematics and Stochastic Analysis
*

*Linear*-

*implicit*versions of strong Taylor numerical schemes for finite dimensional It6 stochastic

*differential*equations (SDEs) are shown to have the same order as the original scheme. ... The combined truncation

*and*global discretization error of an 7 strong

*linear*-

*implicit*Taylor scheme with time-step A applied to the N dimensional It6-Galerkin SDE for a class of parabolic stochastic partial ... thus be of the form KT, UoA'

*and*hence the combined truncation

*and*global discretization error bound will be as asserted in Theorem 2. D ...

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