Zobrazeno 1 - 10
of 125
pro vyhledávání: '"Joseph E. Pasciak"'
Publikováno v:
IMA Journal of Numerical Analysis. 40:1746-1771
In this paper, we develop and study algorithms for approximately solving linear algebraic systems: ${{\mathcal{A}}}_h^\alpha u_h = f_h$, $ 0< \alpha
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ee1d736129750d359c1e792ad94c23bb
https://doi.org/10.1093/imanum/drz013
https://doi.org/10.1093/imanum/drz013
Publikováno v:
Numerische Mathematik. 142:235-278
We propose a new nonconforming finite element algorithm to approximate the solution to the elliptic problem involving the fractional Laplacian. We first derive an integral representation of the bilinear form corresponding to the variational problem.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b43d8f31c184bf5efef7e0db6816b4b6
https://doi.org/10.1007/s00211-019-01025-x
https://doi.org/10.1007/s00211-019-01025-x
Publikováno v:
Computational Methods in Applied Mathematics. 18:1-20
We present and analyze a space-time Petrov–Galerkin finite element method for a time-fractional diffusion equation involving a Riemann–Liouville fractional derivative of order α ∈ ( 0 , 1 ) {\alpha\in(0,1)} in time and zero initial data. We de
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6a54e4f9298a22e9a26ab3016f48f3bc
https://doi.org/10.1515/cmam-2017-0026
https://doi.org/10.1515/cmam-2017-0026
Publikováno v:
Journal of Computational and Applied Mathematics. 315:32-48
We study the numerical approximation of a time dependent equation involving fractional powers of an elliptic operator $L$ defined to be the unbounded operator associated with a Hermitian, coercive and bounded sesquilinear form on $H^1_0(\Omega)$. The
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::09199d9b38a5fd0ae2f4b5e2f566229a
https://doi.org/10.1016/j.cam.2016.10.016
https://doi.org/10.1016/j.cam.2016.10.016
Autor:
Stanislav Harizanov, Pencho Marinov, Svetozar Margenov, Joseph E. Pasciak, Raytcho D. Lazarov
Publikováno v:
Lecture Notes in Computational Science and Engineering ISBN: 9783030142438
The paper is devoted to the numerical solution of algebraic systems of the type \({\mathbb A}^\alpha \mathbf {u}=\mathbf {f}\), 0 < α < 1, where \({\mathbb A}\) is a symmetric and positive definite matrix. We assume that \({\mathbb A}\) is obtained
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d707cde297eb72b85086ea99250f7c63
https://doi.org/10.1007/978-3-030-14244-5_9
https://doi.org/10.1007/978-3-030-14244-5_9
Autor:
Stanislav Harizanov, Svetozar Margenov, Pencho Marinov, Joseph E. Pasciak, Raytcho D. Lazarov
Publikováno v:
Journal of Computational Physics. 408:109285
Here we study theoretically and compare experimentally with the methods developed in [1] , [2] an efficient method for solving systems of algebraic equations A ˜ α u ˜ h = f ˜ h , 0 α 1 , where A ˜ is an N × N matrix coming from the discretiza
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::664632732cb0128d5fb73671bcecde80
https://doi.org/10.1016/j.jcp.2020.109285
https://doi.org/10.1016/j.jcp.2020.109285
Publikováno v:
Mathematics of Computation. 84:2665-2700
In this work, we consider boundary value problems involving either Caputo or Riemann-Liouville fractional derivatives of order α ∈ (1, 2) on the unit interval (0, 1). These fractional derivatives lead to nonsymmetric boundary value problems, which
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::95e0901c837af38cba642a82f3789396
https://doi.org/10.1090/mcom/2960
https://doi.org/10.1090/mcom/2960
Autor:
Joseph E. Pasciak, Andrea Bonito
Publikováno v:
Mathematics of Computation. 84:2083-2110
We present and study a novel numerical algorithm to approximate the action of $T^\beta:=L^{-\beta}$ where $L$ is a symmetric and positive definite unbounded operator on a Hilbert space $H_0$. The numerical method is based on a representation formula
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::927caaeac82f91f6391e6ebeed8f6e8b
https://doi.org/10.1090/s0025-5718-2015-02937-8
https://doi.org/10.1090/s0025-5718-2015-02937-8
We consider the finite element approximation of fractional powers of regularly accretive operators via the Dunford-Taylor integral approach. We use a sinc quadrature scheme to approximate the Balakrishnan representation of the negative powers of the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::49b1a3a86f45bb996a3c62e649a72945
http://arxiv.org/abs/1709.06619
http://arxiv.org/abs/1709.06619
In this paper, we develop a numerical scheme for the space-time fractional parabolic equation, i.e., an equation involving a fractional time derivative and a fractional spatial operator. Both the initial value problem and the non-homogeneous forcing
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c71debf45cd37d3dbeb49c5a6ac0d68d
http://arxiv.org/abs/1704.04254
http://arxiv.org/abs/1704.04254