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Semi-Analytical and Semi-Numerical Methods in Celestial Mechanics

1997
*
International Astronomical Union Colloquium
*

*The*role

*of*numerical analysis tools

*in*analytical

*theories*is briefly discussed. ... Four main ideas behind semi-analytical

*theories*are identified and reviewed: series contraction, analytical support

*of*numerical

*integration*, piecewise solutions, and numerical evaluation

*of*action-angle ... Transforming

*the*

*equations*

*of*motion by averaging, one obtains a slowly evolving system;

*the*system which would cause

*some*

*problems*

*in*further analytical treatment, but which can be

*integrated*numerically ...

##
###
Page 135 of Mathematical Reviews Vol. 51, Issue 1
[page]

1976
*
Mathematical Reviews
*

Howes, On approximate and true solutions

*of*a nonlinear singular*perturbation**problem*(p. 820); Stig-Olof Londen, On*the*variation*of**the*solutions*of*a nonlinear*integral**equation*(p. 821); D. L. ... Miller,*Some*fundamental*theory**of*Volterra*integral*Ae vee (pp. 568-579); J. A. Nohel and D. F. ...##
###
Page 2621 of Mathematical Reviews Vol. , Issue 2000d
[page]

2000
*
Mathematical Reviews
*

For

*some**problems**the*solution*of*this system can be found*in*a special form. Then a first*integral*F can be calculated by*integration*. ...*In*fact, no general*theory*is developed, but to show how this*perturbation*2000d:34113 method works,*the*method is applied to*the*van der Pol*equation*, a Mathieu*equation*, and an*equation*for a harmonic ...##
###
Page 1174 of Mathematical Reviews Vol. , Issue 2000b
[page]

2000
*
Mathematical Reviews
*

These exclusions correspond to

*the*small divisors*in**the**perturbation*series and are*the*reason that one can only prove that*the**perturbed*system behaves like*the*unperturbed one on*some*subset*of*all ... On*the*one hand is*the**theory**of*completely*integrable*systems. These are Hamiltonian systems for which there exist canonical variables*in*which*the*equa- tions*of*motion are explicitly*integrable*. ...##
###
Page 1702 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

MA);
Ono, Kinya (1-BOST; Boston, MA)
On

*the*application*of*geometric singular*perturbation**theory*to*some*classical two-point boundary value*problems*. ... Summary: “*In*this tutorial, we illustrate how geometric singular*perturbation**theory*provides a complementary dynamical systems- based approach to*the*method*of*matched asymptotic expansions for*some*classical ...##
###
Page 136 of Mathematical Reviews Vol. , Issue 84a
[page]

1984
*
Mathematical Reviews
*

Authors’ summary: “We generalize

*the**theory**of*asymptotic*integration**of*singularly*perturbed**problems*, developed earlier for parabolic, hyperbolic, and elliptic*equations*[Lomov, Dokl. Akad. ... Lutz, Robert; Sari, Tewfik 84a:34057 Applications*of*nonstandard analysis to boundary value*problems**in*singular*perturbation**theory*. ...##
###
Page 2668 of Mathematical Reviews Vol. , Issue 84g
[page]

1984
*
Mathematical Reviews
*

*In*

*some*physical

*problems*,

*the*

*perturbations*

*of*impulsive type are more realistic.

*In*this way,

*the*notion

*of*a measure differential

*equation*becomes very natural. ...

*The*

*problem*

*of*when an indefinite

*integral*

*of*an almost periodic function is almost periodic and related questions are discussed

*in*Chapter 6. ...

##
###
On generators of new methods of the perturbation theory

1996
*
Symposium - International astronomical union
*

*In*this article are discussed classical and modern interpretations

*of*

*the*

*perturbation*

*theory*methods. ... We call Ζ(ζ,/,μ) and zo

*the*generators

*of*

*the*

*perturbation*

*theory*for

*problem*(1) and

*equation*(4)

*the*generating

*equation*for

*equation*(1). ... differs from

*the*classical

*perturbation*

*theory*

*in*an essential point:

*the*determination

*of*

*perturbation*/,μ) from

*the*

*equation*(7) does not require

*the*preliminary solving

*of*a generating

*equation*( ...

##
###
Page 1699 of Mathematical Reviews Vol. 57, Issue 5
[page]

1979
*
Mathematical Reviews
*

S. 57 #13105

*Some*results and*problems**of**the**theory**of**the*stability*of**the*~—*of*linear almost periodic*equations*with aftereffect. (Russian Differential*equations*with deviating argument (Proc. ... There is also an introductory chapter on*the**theory**of*linear*integral**equations*. ...##
###
Page 2416 of Mathematical Reviews Vol. , Issue 86f
[page]

1986
*
Mathematical Reviews
*

Lomov,

*Integration**of*singularly*perturbed**problems*by means*of*series that converge not only*in**the*asymptotic sense but also*in**the*usual sense (Russian) (pp. 230-235, 445); A. K. ... Vencovské, On a*problem**in**the**theory**of*linear differential*equations*with quasiperiodic coefficients (pp. 214-217, 444); E. ...##
###
Nonlinear waves in integrable and nonintegrable systems (Mathematical Modeling and Computation 16) By Jianke Yang

2015
*
Bulletin of the London Mathematical Society
*

Such nearly -

doi:10.1112/blms/bdu100
fatcat:ryukenp735b6zmx5edlx2kssim
*integrable**equations*naturally appear*in**the*studies*of*various physical*problems*. ...*In*this chapter, soliton*perturbation**theory*based on asymptotic multiple -scales expansions is developed for*the**perturbed*NLS*equation*. ...*The*fifth chapter moves further away from*integrability*, and deals with*equations*which can not be viewed as*perturbations**of**integrable*models. ...##
###
Page 4089 of Mathematical Reviews Vol. , Issue 83j
[page]

1983
*
Mathematical Reviews
*

Mitropol’skii],

*Integral*manifolds*in**the**theory**of*differential*equations*(pp. 749-775); F. Neuman, Global*theory**of*linear differential*equations**of**the*nth order (pp. 777-794); M. ... Kozlov,*The*method*of*vector Ljapunov functions*in**the*qualitative*theory**of*differential*equations**in*Banach spaces (pp. 685-707); J. ...##
###
Page 5375 of Mathematical Reviews Vol. , Issue 99h
[page]

1999
*
Mathematical Reviews
*

*Some*

*of*

*the*main motivations for studying

*the*

*theory*

*of*those singularly

*perturbed*

*equations*originate from elasticity

*theory*. ... Singular

*perturbations*

*in*

*the*

*theory*

*of*thin elastic rods, 3. ...

##
###
On the Singular Perturbations for Fractional Differential Equation

2014
*
The Scientific World Journal
*

*The*goal

*of*this paper is to examine

*the*possible extension

*of*

*the*singular

*perturbation*differential

*equation*to

*the*concept

*of*fractional order derivative. ... We make use

*of*

*the*Laplace transform operator to derive exact solution

*of*singular

*perturbation*fractional linear differential

*equations*. ... Conflict

*of*Interests

*The*author declares that there is no conflict

*of*interests regarding

*the*publication

*of*this paper. ...

##
###
Page 1428 of Mathematical Reviews Vol. 50, Issue 5
[page]

1975
*
Mathematical Reviews
*

Advances

*in*differential and*integral**equations*. 10389 A collection*of*papers presented at*the*Conference on Qualita- tive*Theory**of*Nonlinear Differential and*Integral**Equations*held at*the*University ... Gustafson, Examples*in**the*oscillation*theory**of*higher order*equations*(p. 203); Frank Hoppensteadt, Asymptotic ex- pansions for singularly*perturbed*systems (pp. 203-204); J. D. ...
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