Zobrazeno 1 - 10
of 929
pro vyhledávání: '"Iserles A"'
We propose a novel framework, called moving window method, for solving the linear Schr\"odinger equation with an external potential in $\mathbb{R}^d$. This method employs a smooth cut-off function to truncate the equation from Cauchy boundary conditi
Externí odkaz:
http://arxiv.org/abs/2408.09463
Autor:
Gao, Jing, Iserles, Arieh
We present an overarching framework for stable spectral methods on a triangle, defined by a multivariate W-system and based on orthogonal polynomials on the triangle. Motivated by the Koornwinder orthogonal polynomials on the triangle, we introduce a
Externí odkaz:
http://arxiv.org/abs/2408.01132
It is often the case that, while the numerical solution of the non-linear dispersive equation $\mathrm{i}\partial_t u(t)=\mathcal{H}(u(t),t)u(t)$ represents a formidable challenge, it is fairly easy and cheap to solve closely related linear equations
Externí odkaz:
http://arxiv.org/abs/2405.04958
Autor:
Iserles, Arieh, Maierhofer, Georg
The efficient approximation of highly oscillatory integrals plays an important role in a wide range of applications. Whilst traditional quadrature becomes prohibitively expensive in the high-frequency regime, Levin methods provide a way to approximat
Externí odkaz:
http://arxiv.org/abs/2404.11448
Autor:
Iserles, Arieh, Kropielnicka, Karolina
This paper considers computational methods that split a vector field into three components in the case when both the vector field and the split components might be unbounded. We first employ classical Taylor expansion which, after some algebra, resul
Externí odkaz:
http://arxiv.org/abs/2403.15147
Autor:
Iserles, Arieh
The contention of this paper is that a spectral method for time-dependent PDEs is basically no more than a choice of an orthonormal basis of the underlying Hilbert space. This choice is governed by a long list of considerations: stability, speed of c
Externí odkaz:
http://arxiv.org/abs/2402.16744
Autor:
Iserles, Arieh, Kropielnicka, Karolina
Using elementary means, we derive the three most popular splittings of $e^{(A+B)}$ and their error bounds in the case when $A$ and $B$ are (possibly unbounded) operators in a Hilbert space, generating strongly continuous semigroups, $e^{tA}$, $e^{tB}
Externí odkaz:
http://arxiv.org/abs/2401.06635
Autor:
Gao, Jing, Iserles, Arieh
The subject of this paper is the design of efficient and stable spectral methods for time-dependent partial differential equations in unit balls. We commence by sketching the desired features of a spectral method, which is defined by a choice of an o
Externí odkaz:
http://arxiv.org/abs/2312.13183
Autor:
Gao, Jing, Iserles, Arieh
We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example is integral
Externí odkaz:
http://arxiv.org/abs/2308.08266
Autor:
Cantero, María José, Iserles, Arieh
We consider polynomials orthogonal on the unit circle with respect to the complex-valued measure $z^{\omega-1}\mathrm{d} z$, where $\omega\in\mathbb{R}\setminus\{0\}$. We derive their explicit form, a generating function and several recurrence relati
Externí odkaz:
http://arxiv.org/abs/2308.06059