Explicit discretization schemes based on NonStandard Finite Differences (NSFD) represent a modication of Standard Finite Differences (SFD) schemes in which the classical denominators step-sizes are usually replaced by particular denominator functions that satisfy certain properties. Sometimes, moreover, a non-local approximation of discrete terms is required. Such numerical schemes may be able to grasp some stability properties of the model analytical solution you are interested in solving, impossible to replicate using classical SFD schemes. The aim of this talk lies in investigating the advantages deriving from the use of NSFD over SFD for some important and representative models of Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs), for which it is a-priori known the behavior of the exact solution. Finally, the possibility of extending the NSFD technique to other differential problems exhibiting positive and oscillating solution is also considered.
On the advantages of nonstandard finite differences discretizations for differential problems
Conte Dajana;Pagano Giovanni
;Paternoster Beatrice
2021-01-01
Abstract
Explicit discretization schemes based on NonStandard Finite Differences (NSFD) represent a modication of Standard Finite Differences (SFD) schemes in which the classical denominators step-sizes are usually replaced by particular denominator functions that satisfy certain properties. Sometimes, moreover, a non-local approximation of discrete terms is required. Such numerical schemes may be able to grasp some stability properties of the model analytical solution you are interested in solving, impossible to replicate using classical SFD schemes. The aim of this talk lies in investigating the advantages deriving from the use of NSFD over SFD for some important and representative models of Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs), for which it is a-priori known the behavior of the exact solution. Finally, the possibility of extending the NSFD technique to other differential problems exhibiting positive and oscillating solution is also considered.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
