The goal of this work is to highlight the advantages of using NonStandard Finite Difference (NSFD) numerical schemes for the solution of ordinary differential equations (ODEs) and Partial Differential Equations (PDEs) of which some properties of the exact solution, such as positivity, are a priori known. The main reference considered is Mickens' work [14], in which the author derives NSFD schemes for ODEs and PDEs that describe real phenomena and, therefore, widely used in applications. We rigorously demonstrate that NSFD methods can have a higher order of convergence than the related classical ones, deriving also conditions that guarantee the stability of the analyzed schemes. Furthermore, we carry out in-depth numerical tests comparing classical methods with the NSFD ones proposed by Mickens, evaluating when the latter are decidedly advantageous.

On the Advantages of Nonstandard Finite Difference Discretizations for Differential Problems

Conte D.;Guarino N.;Pagano G.
;
Paternoster B.
2022

Abstract

The goal of this work is to highlight the advantages of using NonStandard Finite Difference (NSFD) numerical schemes for the solution of ordinary differential equations (ODEs) and Partial Differential Equations (PDEs) of which some properties of the exact solution, such as positivity, are a priori known. The main reference considered is Mickens' work [14], in which the author derives NSFD schemes for ODEs and PDEs that describe real phenomena and, therefore, widely used in applications. We rigorously demonstrate that NSFD methods can have a higher order of convergence than the related classical ones, deriving also conditions that guarantee the stability of the analyzed schemes. Furthermore, we carry out in-depth numerical tests comparing classical methods with the NSFD ones proposed by Mickens, evaluating when the latter are decidedly advantageous.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4804252
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 0
social impact