WebGeneralised Discrete Gronwall Lemmas. Dr. S. McKee, Oxford University Computing Laboratory, 19 Parks Road, Oxford OX 13 PL, England. Search for more papers by this author. ... We present discrete generalisations of the usual Gronwall lemma which are particularly suitable for integral equations with an Abel' type singularity. WebSep 17, 2024 · In the past few decades, the fractional calculus has attracted more and more attention in modelling various applications and various high-order numerical techniques have been developed for the fractional differential systems ... The following discrete Gronwall lemma will be used when proving the convergence of the scheme. Lemma 2.1
Generalized Gronwall inequalities and their applications to …
Web65M12 Stability and convergence of numerical methods Abstract : The well-known Gronwall lemma often serves as a major tool for the analysis of time-dependent problems via … WebApr 11, 2024 · In this paper, a class of discrete Gronwall inequalities is proposed. It is efficiently applied to analyzing the constructed L1/local discontinuous Galerkin (LDG) finite element methods which are used for numerically solving the Caputo-Hadamard time fractional diffusion equation. The derived numerical methods are shown to be $$\\alpha … side effects loestrin fe
A Novel Discrete Fractional Grönwall-Type Inequality and Its ...
WebIn this paper, we consider a system of ordinary differential equations with non-local discrete diffusion and finite delay and with either a finite or an infinite number of equations. We prove several properties of solutions such as comparison, stability and symmetry. We create a numerical simulation showing that this model can be appropriate to model dynamical life … WebJan 1, 2024 · The proof is based on a corresponding deterministic version of the discrete Gronwall lemma and an inequality bounding the supremum in terms of the infimum for … Web65M12 Stability and convergence of numerical methods Abstract : The well-known Gronwall lemma often serves as a major tool for the analysis of time-dependent problems via energy methods. However, there is the need for a similar tool when considering temporal discretizations of evolutionary problems. side effects lipitor weight gain