dr inż. Anna Szafrańska
- Department of Differential Equations and Mathematical Applications
- Faculty of Applied Physics and Mathematics
On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation
In this note, we establish the property of convergence for a finite-difference discretization of a diffusive partial differential equation with generalized Burgers convective law and generalized Hodgkin–Huxley reaction. The numerical method was previously investigated in the literature and, amongst other features of interest, it is a fast and nonlinear technique that is capable of preserving positivity, boundedness and monotonicity....
In this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties
Starting from the Riemann–Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation. Discussing in full generality the existence of such operator over continuous functions, we derive some obstruction Lemma which can be used to prove the triviality...
Obtained scientific degrees/titles
Obtained science degreedr inż. Mathematics (Mathematics)Uniwersytet Gdański, Wydział Matematyki, Fizyki i Informatyki
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