The present paper concerns the numerical solution of time-fractional reaction–advection–diffusion problems. In real applications, an important issue is the preservation of qualitative properties of the analytical solution, such as positivity, which standard methods achieve only for small stepsizes. Here, novel explicit and implicit non-standard finite difference methods are introduced, by treating different terms in the approximations on different time levels, in a way to keep the solution non-negative at all times. A rigorous analysis of the stability and convergence of the proposed schemes is provided, offering robust theoretical results that illustrate their effectiveness in preserving positivity while generating accurate approximations of the solution. Finally, some numerical experiments demonstrate the efficacy of the proposed methods on different benchmark problems.

Non-standard schemes for time-fractional reaction–advection–diffusion problems

Cardone A.;Frasca Caccia G.
;
Paternoster B.
2025

Abstract

The present paper concerns the numerical solution of time-fractional reaction–advection–diffusion problems. In real applications, an important issue is the preservation of qualitative properties of the analytical solution, such as positivity, which standard methods achieve only for small stepsizes. Here, novel explicit and implicit non-standard finite difference methods are introduced, by treating different terms in the approximations on different time levels, in a way to keep the solution non-negative at all times. A rigorous analysis of the stability and convergence of the proposed schemes is provided, offering robust theoretical results that illustrate their effectiveness in preserving positivity while generating accurate approximations of the solution. Finally, some numerical experiments demonstrate the efficacy of the proposed methods on different benchmark problems.
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/11386/4909597
 Attenzione

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

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