scholarly journals Projected explicit and implicit Taylor series methods for DAEs

2021 ◽  
Author(s):  
Diana Estévez Schwarz ◽  
René Lamour
Keyword(s):  
Taylor Series ◽  
Multibody Systems ◽  
Optimization Problem ◽  
Automatic Differentiation ◽  
Taylor Coefficients ◽  
Integration Schemes ◽  
Consistent Initial Values ◽  
Taylor Series Methods ◽  
Systems Simulation ◽  
Derivative Array

AbstractThe recently developed new algorithm for computing consistent initial values and Taylor coefficients for DAEs using projector-based constrained optimization opens new possibilities to apply Taylor series integration methods. In this paper, we show how corresponding projected explicit and implicit Taylor series methods can be adapted to DAEs of arbitrary index. Owing to our formulation as a projected optimization problem constrained by the derivative array, no explicit description of the inherent dynamics is necessary, and various Taylor integration schemes can be defined in a general framework. In particular, we address higher-order Padé methods that stand out due to their stability. We further discuss several aspects of our prototype implemented in Python using Automatic Differentiation. The methods have been successfully tested on examples arising from multibody systems simulation and a higher-index DAE benchmark arising from servo-constraint problems.

scholarly journals A note on a space Hp, a of holomorphic functions

1987 ◽  
Vol 35 (3) ◽  
pp. 471-479
Author(s):  
H. O. Kim ◽  
S. M. Kim ◽  
E. G. Kwon
Keyword(s):  
Hardy Space ◽  
Complex Plane ◽  
Unit Disc ◽  
Weak Type ◽  
Holomorphic Functions ◽  
Embedding Theorem ◽  
Type Operator ◽  
Taylor Coefficients ◽  
Bounded Holomorphic

For 0 < p < ∞ and 0 ≤a; ≤ 1, we define a space Hp, a of holomorphic functions on the unit disc of the complex plane, for which Hp, 0 = H∞, the space of all bounded holomorphic functions, and Hp, 1 = Hp, the usual Hardy space. We introduce a weak type operator whose boundedness extends the well-known Hardy-Littlewood embedding theorem to Hp, a, give some results on the Taylor coefficients of the functions of Hp, a and show by an example that the inner factor cannot be divisible in Hp, a.

scholarly journals BOUNDARY ANGULAR DERIVATIVES OF GENERALIZED SCHUR FUNCTIONS

2012 ◽  
Vol 93 (3) ◽  
pp. 203-224
Author(s):  
VLADIMIR BOLOTNIKOV ◽  
TENGYAO WANG ◽  
JOSHUA M. WEISS
Keyword(s):  
Schur Functions ◽  
Taylor Coefficients ◽  
Generalized Schur Functions ◽  
Angular Derivatives ◽  
Derivatives Of

AbstractCharacterization of generalized Schur functions in terms of their Taylor coefficients was established by Krein and Langer [‘Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im Raume ${\Pi }_{\kappa } $ zusammenhängen. I. Einige Funktionenklassen und ihre Darstellungen’, Math. Nachr. 77 (1977), 187–236]. We establish a boundary analogue of this characterization.

Similarité Entre Certains Quotients de A+et des Quotients D'Algèbres Uniformes

1991 ◽  
Vol 34 (4) ◽  
pp. 485-491
Author(s):  
Konin Koua
Keyword(s):  
Convergent Series ◽  
Disc Algebra ◽  
Taylor Coefficients

RésuméLetA(D) be the usual disc algebra, and letA+be the subalgebra ofA(D) consisting in thosef € A(D) which have an absolutely convergent series of Taylor coefficients. Setm1= {f€A(D) |f(1) = 0},m=m1∩A+, letGbe the functionandK = A+∩ I1.We show that the quotient algebrasm1/I1andm/Kare similar in the sense of J. Esterle.

scholarly journals On a class of shift-invariant subspaces of the Drury-Arveson space

2018 ◽  
Vol 5 (1) ◽  
pp. 1-8
Author(s):  
Nicola Arcozzi ◽  
Matteo Levi
Keyword(s):  
Invariant Subspace ◽  
Invariant Subspaces ◽  
Hankel Operators ◽  
Taylor Coefficients ◽  
The Right ◽  
Arveson Space

Abstract In the Drury-Arveson space, we consider the subspace of functions whose Taylor coefficients are supported in a set Y⊂ ℕd with the property that ℕ\X + ej ⊂ ℕ\X for all j = 1, . . . , d. This is an easy example of shift-invariant subspace, which can be considered as a RKHS in is own right, with a kernel that can be explicitly calculated for specific choices of X. Every such a space can be seen as an intersection of kernels of Hankel operators with explicit symbols. Finally, this is the right space on which Drury’s inequality can be optimally adapted to a sub-family of the commuting and contractive operators originally considered by Drury.

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