Zobrazeno 1 - 10
of 650
pro vyhledávání: '"65N35"'
In this paper, we establish a superconvergence property of Galerkin approximations to some non-linear Schr\"odinger equations of Gross-Pitaevskii type. More precisely, denoting by $u^*\in X \subseteq H^1(\Omega)$ the exact solution to such an equatio
Externí odkaz:
http://arxiv.org/abs/2502.07638
Autor:
Dũng, Dinh
We proved convergence rates of fully discrete multi-level simultaneous linear collocation approximation of solutions to parametric elliptic PDEs on bounded polygonal domain with log-normal random inputs based on a finite number of their values at poi
Externí odkaz:
http://arxiv.org/abs/2502.07799
Autor:
Hu, Hao, Yu, Haijun
Hermite polynomials and functions have extensive applications in scientific and engineering problems. While it is recognized that employing the scaled Hermite functions rather than the standard ones can remarkably enhance the approximation performanc
Externí odkaz:
http://arxiv.org/abs/2412.08044
Recently, general fractional calculus was introduced by Kochubei (2011) and Luchko (2021) as a further generalisation of fractional calculus, where the derivative and integral operator admits arbitrary kernel. Such a formalism will have many applicat
Externí odkaz:
http://arxiv.org/abs/2411.08080
Dirichlet-Neumann Operators (DNOs) are important to the formulation, analysis, and simulation of many crucial models found in engineering and the sciences. For instance, these operators permit moving-boundary problems, such as the classical water wav
Externí odkaz:
http://arxiv.org/abs/2410.19296
Convection-diffusion-reaction equations are a class of second-order partial differential equations widely used to model phenomena involving the change of concentration/population of one or more substances/species distributed in space. Understanding a
Externí odkaz:
http://arxiv.org/abs/2410.11669
A machine-learnable variational scheme using Gaussian radial basis functions (GRBFs) is presented and used to approximate linear problems on bounded and unbounded domains. In contrast to standard mesh-free methods, which use GRBFs to discretize stron
Externí odkaz:
http://arxiv.org/abs/2410.06219
Autor:
Nicholls, David, Zhu, Tianyu
Over the past twenty years, the field of plasmonics has been revolutionized with the isolation and utilization of two--dimensional materials, particularly graphene. Consequently there is significant interest in rapid, robust, and highly accurate comp
Externí odkaz:
http://arxiv.org/abs/2410.05483
This paper presents a point-wise divergence-free projection method for numerical approximations of photonic quasicrystals problems. The original three-dimensional quasiperiodic Maxwell's system is transformed into a periodic one in higher dimensions
Externí odkaz:
http://arxiv.org/abs/2409.05528
Autor:
Bartel, Felix, Dũng, Dinh
We proved convergence rates of linear sampling recovery of functions in an abstract Bochner space satisfying some weighted $\ell_2$-summability of their generalized polynomial chaos expansion coefficients, by extended least squares methods. As applic
Externí odkaz:
http://arxiv.org/abs/2409.05050