Zobrazeno 1 - 10
of 209
pro vyhledávání: '"A, Płóciniczak"'
Publikováno v:
Journal of Computational and Applied Mathematics 458 (2025), 116343
We consider a nonlocal functional equation that is a generalization of the mathematical model used in behavioral sciences. The equation is built upon an operator that introduces a convex combination and a nonlinear mixing of the function arguments. W
Externí odkaz:
http://arxiv.org/abs/2411.01862
Autor:
del Teso, Félix, Płociniczak, Łukasz
Publikováno v:
Applied Mathematics Letters 161 (2025), 109364
We establish uniform error bounds of the L1 discretization of the Caputo derivative of H\"older continuous functions. The result can be understood as: error = (degree of smoothness - order of the derivative). We present an elementary proof and illust
Externí odkaz:
http://arxiv.org/abs/2411.10833
Publikováno v:
Applied Mathematics and Computation 477 (2024), 128798
In this paper, we examine the solvability of a functional equation in a Lipschitz space. As an application, we use our result to determine the existence and uniqueness of solutions to an equation describing a specific type of choice behavior model fo
Externí odkaz:
http://arxiv.org/abs/2405.12345
Autor:
Płociniczak, Łukasz, Teuerle, Marek A.
The fractional material derivative appears as the fractional operator that governs the dynamics of the scaling limits of L\'evy walks - a stochastic process that originates from the famous continuous-time random walks. It is usually defined as the Fo
Externí odkaz:
http://arxiv.org/abs/2402.19015
Autor:
Jaszczak, Bogna, Płociniczak, Łukasz
This paper presents an extension of Keller's classical model to address the dynamics of long-distance trail running, a sport characterized by varying terrains, changing elevations, and the critical influence of in-race nutrition uptake. The optimizat
Externí odkaz:
http://arxiv.org/abs/2401.02919
Autor:
del Teso, Félix, Płociniczak, Łukasz
We consider a general family of nonlocal in space and time diffusion equations with space-time dependent diffusivity and prove convergence of finite difference schemes in the context of viscosity solutions under very mild conditions. The proofs, base
Externí odkaz:
http://arxiv.org/abs/2311.14317
We construct a Convolution Quadrature (CQ) scheme for the quasilinear subdiffusion equation and supply it with the fast and oblivious implementation. In particular we find a condition for the CQ to be admissible and discretize the spatial part of the
Externí odkaz:
http://arxiv.org/abs/2311.00081
We couple the L1 discretization of the Caputo fractional derivative in time with the Galerkin scheme to devise a linear numerical method for the semilinear subdiffusion equation. Two important points that we make are: nonsmooth initial data and time-
Externí odkaz:
http://arxiv.org/abs/2310.04246
The time-fractional porous medium equation is an important model of many hydrological, physical, and chemical flows. We study its self-similar solutions, which make up the profiles of many important experimentally measured situations. We prove that t
Externí odkaz:
http://arxiv.org/abs/2303.01725
Publikováno v:
In Journal of Computational and Applied Mathematics April 2025 458
