18 citations · 18 across the 4 of their papers we have counts for
9 papers
The Bushell-Okrasiński inequality
Łukasz Płociniczak
We present an expository account of the Bushell-Okrasiński inequality, the motivation behind it, its history, and several generalizations. This inequality originally appeared in st…
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…
Stability of fixed points in an approximate solution of the spring-mass running model
Zofia Wróblewska, Piotr Kowalczyk, Łukasz Płociniczak
We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large…
Asymptotic behaviour of a solution to a nonlinear equation modelling capillary rise
Łukasz Płociniczak, Mateusz Świtała
We are concerned with the asymptotics and perturbation analysis of a singular second-order nonlinear ODE that models capillary rise of a fluid inside a narrow vertical tube. We pro…
A weighted finite difference method for subdiffusive Black Scholes Model
Grzegorz Krzyżanowski, Marcin Magdziarz, Łukasz Płociniczak
In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in…
Asymptotic analysis of internal relaxation-oscillations in a conceptual climate model
Łukasz Płociniczak
We construct a dynamical system based on the KCG (Källén, Crafoord, Ghil) conceptual climate model which includes the ice-albedo and precipitation-temperature feedbacks. Further, w…