The $\star $-product approach for linear ODEs: A numerical study of the scalar case

Pozza, Stefano; Van Buggenhout, Niel

Displaying similar documents to “The $☆$ -product approach for linear ODEs: A numerical study of the scalar case”

The only continuous Volterra right inverses in $C_{c} [0, 1]$ of the operator $d / d t$ are $ʃ_{a}^{t}$

D. Przeworska-Rolewicz, S. Rolewicz (1987)

Colloquium Mathematicae

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Numerical solution of Black-Scholes option pricing with variable yield discrete dividend payment

Rafael Company, Lucas Jódar, Enrique Ponsoda (2008)

Banach Center Publications

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This paper deals with the construction of numerical solution of the Black-Scholes (B-S) type equation modeling option pricing with variable yield discrete dividend payment at time $t_{d}$ . Firstly the shifted delta generalized function $δ (t - t_{d})$ appearing in the B-S equation is approximated by an appropriate sequence of nice ordinary functions. Then a semidiscretization technique applied on the underlying asset is used to construct a numerical solution. The limit of this numerical solution is independent...

The joint essential numerical range of operators: convexity and related results

Chi-Kwong Li, Yiu-Tung Poon (2009)

Studia Mathematica

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Let W(A) and $W_{e} (A)$ be the joint numerical range and the joint essential numerical range of an m-tuple of self-adjoint operators A = (A₁, ..., Aₘ) acting on an infinite-dimensional Hilbert space. It is shown that $W_{e} (A)$ is always convex and admits many equivalent formulations. In particular, for any fixed i ∈ 1, ..., m, $W_{e} (A)$ can be obtained as the intersection of all sets of the form $c l (W (A ₁, . . ., A_{i + 1}, A_{i} + F, A_{i + 1}, . . ., A ₘ))$ , where F = F* has finite rank. Moreover, the closure cl(W(A)) of W(A) is always star-shaped with the elements in...

On the power boundedness of certain Volterra operator pencils

Dashdondog Tsedenbayar (2003)

Studia Mathematica

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Let V be the classical Volterra operator on L²(0,1), and let z be a complex number. We prove that I-zV is power bounded if and only if Re z ≥ 0 and Im z = 0, while I-zV² is power bounded if and only if z = 0. The first result yields $| | (I - V) ⁿ - {(I - V)}^{n + 1} | | = O (n^{- 1 / 2})$ as n → ∞, an improvement of [Py]. We also study some other related operator pencils.

On $^{γ (\cdot, \cdot)}$ -subdifferentiable and [+γ]-subdifferentiable Functions

S. Rolewicz (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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On the fundamental solution of the equation $∆^{p} u (X) + k (r) u (X) = 0$

J. Musiałek (1969)

Annales Polonici Mathematici

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A singular initial value problem for the equation $u^{(n)} (x) = g (u (x))$

Wojciech Mydlarczyk (1998)

Annales Polonici Mathematici

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We consider the problem of the existence of positive solutions u to the problem $u^{(n)} (x) = g (u (x))$ , $u (0) = u^{'} (0) = . . . = u^{(n - 1)} (0) = 0$ (g ≥ 0,x > 0, n ≥ 2). It is known that if g is nondecreasing then the Osgood condition $\int ₀^{δ} 1 / s {[s / g (s)]}^{1 / n} d s < \infty$ is necessary and sufficient for the existence of nontrivial solutions to the above problem. We give a similar condition for other classes of functions g.

- and $^{\infty}$ -hypoellipticity of partial differential operators with constant Colombeau coefficients

Claudia Garetto (2010)

Banach Center Publications

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We provide a deep investigation of the notions of - and $^{\infty}$ -hypoellipticity for partial differential operators with constant Colombeau coefficients. This involves generalized polynomials and fundamental solutions in the dual of a Colombeau algebra. Sufficient conditions and necessary conditions for - and $^{\infty}$ -hypoellipticity are given

Mobile TeX: Porting TeX to the iPad

Arthur Reutenauer (2011)

Zpravodaj Československého sdružení uživatelů TeXu

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The paper presents the achievement of Richard Koch, amongst others author of TeXShop and MacTeX developer, who has successfully compiled and used TeX on Apple's iPad.

Some results on derangement polynomials

Mehdi Hassani, Hossein Moshtagh, Mohammad Ghorbani (2022)

Commentationes Mathematicae Universitatis Carolinae

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We study moments of the difference $D_{n} (x) - x^{n} n! e^{- 1 / x}$ concerning derangement polynomials $D_{n} (x)$ . For the first moment, we obtain an explicit formula in terms of the exponential integral function and we show that it is always negative for $x > 0$ . For the higher moments, we obtain a multiple integral representation of the order of the moment under computation.

Time regularity and functions of the Volterra operator

Zoltán Léka (2014)

Studia Mathematica

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Our aim is to prove that for any fixed 1/2 < α < 1 there exists a Hilbert space contraction T such that σ(T) = 1 and $| | T^{n + 1} - T ⁿ | | ≍ (n \geq 1)$ . This answers Zemánek’s question on the time regularity property.

Some hypergeometric polynomials associated with the Lauricella function $F_{D}$ of several variables. I

L. Carlitz, H. M. Srivastava (1976)

Matematički Vesnik

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Some hypergeometric polynomials associated with the Lauricella function $F_{D}$ of several variables. II

L. Carlitz, H. M. Srivastava (1976)

Matematički Vesnik

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Duality in $N = 2$ Susy $S U (2)$ Yang-Mills Theory : A Pedagogical Introduction to the Work of Seiberg and Witten

Adel Bilal (1997)

Recherche Coopérative sur Programme n°25

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A Green's function for θ-incomplete polynomials

Joe Callaghan (2007)

Annales Polonici Mathematici

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Let K be any subset of $ℂ^{N}$ . We define a pluricomplex Green’s function $V_{K, θ}$ for θ-incomplete polynomials. We establish properties of $V_{K, θ}$ analogous to those of the weighted pluricomplex Green’s function. When K is a regular compact subset of $ℝ^{N}$ , we show that every continuous function that can be approximated uniformly on K by θ-incomplete polynomials, must vanish on $K ∖ s u p p {(d d^{c} V_{K, θ})}^{N}$ . We prove a version of Siciak’s theorem and a comparison theorem for θ-incomplete polynomials. We compute $s u p p {(d d^{c} V_{K, θ})}^{N}$ when K is a compact...