90 citations · 188 across the 16 of their papers we have counts for
7 papers · 1 filter
Time-fractional porous medium equation: Erdélyi-Kober integral equations, compactly supported solutions, and numerical methods
Belen López, Hanna Okrasińska-Płociniczak, Łukasz Płociniczak +1
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…
Error of the Galerkin scheme for a semilinear subdiffusion equation with time-dependent coefficients and nonsmooth data
Łukasz Płociniczak
We investigate the error of the (semidiscrete) Galerkin method applied to a semilinear subdiffusion equation in the presence of a nonsmooth initial data. The diffusion coefficient…
On a discrete composition of the fractional integral and Caputo derivative
Łukasz Płociniczak
We prove a discrete analogue for the composition of the fractional integral and Caputo derivative. This result is relevant in numerical analysis of fractional PDEs when one discret…
Linear Galerkin-Legendre spectral scheme for a degenerate nonlinear and nonlocal parabolic equation arising in climatology
Łukasz Płociniczak
A special place in climatology is taken by the so-called conceptual climate models. These relatively simple sets of differential equations can successfully describe single mechanis…
Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line
Hanna Okrasińska-Płociniczak, Łukasz Płociniczak
Many physical, biological, and economical systems exhibit various memory effects due to which their present state depends on the history of the whole evolution. Combined with the n…
Numerical method for the time-fractional porous medium equation
Łukasz Płociniczak
This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits bot…
Finite difference method for a Volterra equation with a power-type nonlinearity
Hanna Okrasińska-Płociniczak, Łukasz Płociniczak
In this work we prove that a family of explicit numerical finite-difference methods is convergent when applied to a nonlinear Volterra equation with a power-type nonlinearity. In t…