Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Sheehan Olver"'
We present a numerical approach for computing attractive-repulsive power law equilibrium measures in arbitrary dimension. We prove new recurrence relationships for radial Jacobi polynomials on $d$-dimensional ball domains, providing a substantial gen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::88e950ffb62c312974c3beb64caa98c9
http://hdl.handle.net/10044/1/101089
http://hdl.handle.net/10044/1/101089
Autor:
Yuan Xu, Sheehan Olver
Publikováno v:
Integral Transforms and Special Functions. 32:604-619
The wave equation $\left(\partial_{tt} - c^2 \Delta_x\right) u(x,t) = e^{-t} f(x,t)$ is shown to have a unique solution if $u$ and its partial derivatives in $x$ are in $L^2(e^{-t})$ on the cone, and the solution can be explicit given in the Fourier
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8801f965fdb4e807e29374d4d7c37fdf
https://doi.org/10.1080/10652469.2020.1808633
https://doi.org/10.1080/10652469.2020.1808633
Autor:
Yuan Xu, Sheehan Olver
Publikováno v:
Mathematics of Computation. 89:2847-2865
We present explicit constructions of orthogonal polynomials inside quadratic bodies of revolution, including cones, hyperboloids, and paraboloids. We also construct orthogonal polynomials on the surface of quadratic surfaces of revolution, generalizi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5c79e4f9b5a7df8226d151acdd57dbf5
https://doi.org/10.1090/mcom/3544
https://doi.org/10.1090/mcom/3544
Autor:
Timon S. Gutleb, Sheehan Olver
Publikováno v:
SIAM Journal on Numerical Analysis. 58:1993-2018
We introduce and analyse a sparse spectral method for the solution of Volterra integral equations using bivariate orthogonal polynomials on a triangle domain. The sparsity of the Volterra operator on a weighted Jacobi basis is used to achieve high ef
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9a1f1a4cbc0cab7066edb27c0cb4d1ff
https://doi.org/10.1137/19m1267441
https://doi.org/10.1137/19m1267441
We construct bivariate orthogonal polynomials (OPs) on algebraic curves of the form $y^m = \phi(x)$ in $\mathbb{R}^2$ where $m = 1, 2$ and $\phi$ is a polynomial of arbitrary degree $d$, in terms of univariate semiclassical OPs. We compute connection
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c600a2c3c7a26f9ffdc8dc489deb460f
Orthogonal polynomials in two variables on cubic curves are considered. For an integral with respect to an appropriate weight function defined on a cubic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of or
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3a89a5f7f491088b0d47d2323a4935ec
http://hdl.handle.net/10044/1/90947
http://hdl.handle.net/10044/1/90947
Autor:
Sheehan Olver, Ben Snowball
Publikováno v:
Transactions of Mathematics and Its Applications. 5
In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the methodology to a hi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0754c818d0f0779fd36525291b9e8c8c
https://doi.org/10.1093/imatrm/tnab001
https://doi.org/10.1093/imatrm/tnab001
We review recent advances in algorithms for quadrature, transforms, differential equations and singular integral equations using orthogonal polynomials. Quadrature based on asymptotics has facilitated optimal complexity quadrature rules, allowing for
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::03985a37bd230bf9b9f84887816d742f
http://hdl.handle.net/10044/1/85269
http://hdl.handle.net/10044/1/85269
Autor:
Sheehan Olver, Ben Snowball
Sparse spectral methods for solving partial differential equations have been derived in recent years using hierarchies of classical orthogonal polynomials on intervals, disks, and triangles. In this work we extend this methodology to a hierarchy of n
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::929b0eb24a4285660915029dbdb50c7f
http://hdl.handle.net/10044/1/77304
http://hdl.handle.net/10044/1/77304
Publikováno v:
Lecture Notes in Computational Science and Engineering ISBN: 9783030396466
ICOSAHOM 2018
ICOSAHOM 2018
This paper derives sparse recurrence relations between orthogonal polynomials on a triangle and their partial derivatives, which are analogous to recurrence relations for Jacobi polynomials. We derive these recurrences in a systematic fashion by intr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::29df377ddb67a533aae0a44ad33bfff2
https://doi.org/10.1007/978-3-030-39647-3_5
https://doi.org/10.1007/978-3-030-39647-3_5