ŁP
Łukasz Płociniczak
cs.NAmath.NAmath.APmath.CAmath.DSPartial differential equation (PDE)Cornea data-setCorneal topographyElasticity coefficientmath.FA
On Valency
published · living versionsW_7h4sxp6z·v1 · currentpublished
Structure-Preserving Numerical Schemes for a Time-Fractional Porous Medium Equation with Nonlocal Pressure
with Hubert Woszczek
1 version
Preprints & journals
44 papers in the corpus · 2011–2026Structure-Preserving Numerical Schemes for a Time-Fractional Porous Medium Equation with Nonlocal Pressure2610.27172v2 · \Lukasz P\lociniczak, Hubert Woszczek2026 · 0 citationsarXivon Valency
Error of discretization of Caputo fractional derivative in weighted spaces2604.22470v1 · \Lukasz P\lociniczak, Hubert Woszczek2026 · 0 citationsarXiv
Self-similar solutions to the time-fractional Porous-Medium Equation2604.09281v1 · David G'omez-Castro, \Lukasz P\lociniczak, Juan Luis V'azquez2026 · 0 citationsarXiv
A Unified Model for Blood and Lymph Flow with Coupled Nonsmooth Biochemical Dynamics2603.00779v1 · Bogna Jaszczak-Dyka, \Lukasz P\lociniczak2026 · 0 citationsarXiv
Asymmetric Lévy walks driven by convex combination of fractional material derivatives2602.02169v1 · \Lukasz P\lociniczak, Marek A. Teuerle, Hubert Woszczek2026 · 0 citationsarXiv
Parareal in time and spectral in space fast L1 quasilinear subdiffusion solver2510.11023v1 · Josefa Caballero, \Lukasz P\lociniczak, Kishin Sadarangani2025 · 0 citationsarXiv
Generalized capillary-rise models: existence and fast solvers in integral Hölder spaces2510.05801v1 · Josefa Caballero, \Lukasz P\lociniczak, Kishin Sadarangani2025 · 0 citationsarXiv
Barenblatt solutions for the time-fractional porous medium equation: approach via integral equations2507.19217v1 · Josefa Caballero, Hanna Okrasi'nska-P\lociniczak, \Lukasz P\lociniczak et al.2025 · 0 citationsarXiv
Functional equation arising in behavioral sciences: solvability and collocation scheme in Hölder spaces2502.15324v1 · Josefa Caballero, Hanna Okrasi'nska-P\lociniczak, \Lukasz P\lociniczak et al.2025 · 0 citationsApplied Numerical Mathematics 212 (2025), 268-282
A note on the L1 discretization error for the Caputo derivative in Hölder spaces2411.10833v1 · F'elix del Teso, \Lukasz P\lociniczak2024 · 4 citationsApplied Mathematics Letters 161 (2025), 109364
Collocation method for a functional equation arising in behavioral sciences2411.01862v1 · Josefa Caballero, Hanna Okrasi'nska-P\lociniczak, \Lukasz P\lociniczak et al.2024 · 1 citationJournal of Computational and Applied Mathematics 458 (2025), 116343
Existence and uniqueness of solutions in the Lipschitz space of a functional equation and its application to the behavior of the paradise fish2405.12345v1 · Josefa Caballero, \Lukasz P\lociniczak, Kishin Sadarangani2024 · 7 citationsApplied Mathematics and Computation 477 (2024), 128798
Fractional material derivative: pointwise representation and a finite volume numerical scheme2402.19015v1 · \Lukasz P\lociniczak, Marek A. Teuerle2024 · 0 citationsarXiv
Optimal strategy for trail running with nutrition and fatigue factors2401.02919v1 · Bogna Jaszczak, \Lukasz P\lociniczak2024 · 1 citationarXiv
Numerical methods and regularity properties for viscosity solutions of nonlocal in space and time diffusion equations2311.14317v1 · F'elix del Teso, \Lukasz P\lociniczak2023 · 0 citationsarXiv
Convolution Quadrature for the quasilinear subdiffusion equation2311.00081v3 · Maria L'opez-Fern'andez, \Lukasz P\lociniczak2023 · 3 citationsarXiv
Fully discrete Galerkin scheme for a semilinear subdiffusion equation with nonsmooth data and time-dependent coefficient2310.04246v1 · \Lukasz P\lociniczak, Kacper Ta'zbierski2023 · 3 citationsarXiv
Time-fractional porous medium equation: Erdélyi-Kober integral equations, compactly supported solutions, and numerical methods2303.01725v1 · Belen L'opez, Hanna Okrasi'nska-P\lociniczak, \Lukasz P\lociniczak et al.2023 · 5 citationsarXiv
The Bushell-Okrasiński inequality2203.15256v1 · \Lukasz P\lociniczak2022 · 0 citationsarXiv
Error of the Galerkin scheme for a semilinear subdiffusion equation with time-dependent coefficients and nonsmooth data2202.13728v1 · \Lukasz P\lociniczak2022 · 7 citationsarXiv
Numerical scheme for Erdélyi-Kober fractional diffusion equation using Galerkin-Hermite method2202.06156v1 · \Lukasz P\lociniczak, Mateusz 'Swita\la2022 · 8 citationsarXiv
On a discrete composition of the fractional integral and Caputo derivative2107.10489v3 · \Lukasz P\lociniczak2021 · 4 citationsCommunications in Nonlinear Science and Numerical Simulation 108 (2022), 106234
A linear Galerkin numerical method for a quasilinear subdiffusion equation2107.10057v3 · \Lukasz P\lociniczak2021 · 10 citationsApplied Numerical Mathematics 185 (2023), 203-220
Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line2106.05138v2 · Hanna Okrasi'nska-P\lociniczak, \Lukasz P\lociniczak2021 · 5 citationsApplied Mathematics and Computation 424C (2022), 127033
Linear Galerkin-Legendre spectral scheme for a degenerate nonlinear and nonlocal parabolic equation arising in climatology2106.05140v2 · \Lukasz P\lociniczak2021 · 6 citationsApplied Numerical Mathematics 179 (2022), 105-124
Stability of fixed points in an approximate solution of the spring-mass running model2105.07188v1 · Zofia Wr'oblewska, Piotr Kowalczyk, \Lukasz P\lociniczak2021 · 3 citationsarXiv
Off-axis vortex beam propagation through classical optical system in terms of Kummer confluent hypergeometric function2005.05136v1 · Ireneusz Augustyniak, Weronika Lamperska, Jan Masajada et al.2020 · 2 citationsarXiv
Asymptotic behaviour of a solution to a nonlinear equation modelling capillary rise1907.11434v1 · \Lukasz P\lociniczak, Mateusz 'Swita\la2019 · 4 citationsarXiv
A weighted finite difference method for subdiffusive Black Scholes Model1907.00297v4 · Grzegorz Krzyżanowski, Marcin Magdziarz, \Lukasz P\lociniczak2019 · 23 citationsComputers & Mathematics with Applications 80.5 (2020): 653-670
Solution and asymptotic analysis of a boundary value problem in the spring-mass model of running1903.02247v1 · \Lukasz P\lociniczak, Zofia Wr'oblewska2019 · 0 citationsarXiv
Asymptotic analysis of internal relaxation-oscillations in a conceptual climate model1902.03467v1 · \Lukasz P\lociniczak2019 · 3 citationsarXiv
Derivation of the nonlocal pressure form of the fractional porous medium equation in the hydrological setting1812.08058v1 · \Lukasz P\lociniczak2018 · 18 citationsCommunications in Nonlinear Science and Numerical Simulation 76C (2019), 66-70
Numerical method for the time-fractional porous medium equation1805.10782v1 · \Lukasz P\lociniczak2018 · 19 citationsSIAM Journal on Numerical Analysis, 57(2)(2019), 638-656
Compactly supported solution of the time-fractional porous medium equation on the half-line1803.03016v2 · \Lukasz P\lociniczak, Mateusz 'Swita\la2018 · 0 citationsarXiv
Hopf bifurcation in a conceptual climate model with ice-albedo and precipitation-temperature feedbacks1801.09087v2 · \Lukasz P\lociniczak2018 · 0 citationsarXiv
Quickest drift change detection in Lévy-type force of mortality model1801.00333v1 · MichałKrawiec, Zbigniew Palmowski, \Lukasz P\lociniczak2017 · 2 citationsarXiv
Finite difference method for a Volterra equation with a power-type nonlinearity1705.03073v1 · Hanna Okrasi'nska-P\lociniczak, \Lukasz P\lociniczak2017 · 9 citationsApplied Mathematics and Computation 337 (2018), 452-460
Analysis of cornea curvature using radial basis functions - Part I: Methodology.27614697 · Griffiths, G W, Płociniczak, Ł, Schiesser, W E2017 · 37 citationsComputers in biology and medicine. 2016;77:274-84
Analysis of cornea curvature using radial basis functions - Part II: Fitting to data-set.27570056 · Griffiths, G W, Płociniczak, Ł, Schiesser, W E2017 · 10 citationsComputers in biology and medicine. 2016;77:285-96
Analytical model of the optical vortex microscope.27140125 · Płocinniczak, Łukasz, Popiołek-Masajada, Agnieszka, Masajada, Jan et al.2018 · 38 citationsApplied optics. 2016;55(12):B20-7
Analytical studies of a time-fractional porous medium equation. Derivation, approximation and applications1409.1825v1 · \Lukasz P\lociniczak2014 · 88 citationsarXiv
ODE/PDE analysis of corneal curvature.25113914 · Płociniczak, Lukasz, Griffiths, Graham W, Schiesser, William E2015 · 13 citationsComputers in biology and medicine. 2014;53:30-41
On fractional Bessel equation and the description of corneal topography1201.2526v2 · Wojciech Okrasi'nski, \Lukasz P\lociniczak2012 · 3 citationsarXiv
Bessel Function Model for Corneal Topography1111.6143v2 · Wojciech Okrasi'nski, \Lukasz P\lociniczak2011 · 3 citationsApplied Mathematics and Computation 223 (2013), 436-443
Career total: 76 works. 44 are in this corpus.
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