Discretization schemes based on NonStandard Finite Differences (NSFD) are a modification of Standard Finite Differences (SFD) schemes in which the classical denominators are usually replaced by particular denominator functions that satisfy certain conditions. The main objective of such schemes is to be able to grasp some stability properties of the model analytical solution we are interested to solve, which we are not able to replicate with the classical SFD schemes. We want to investigate the advantages that come from using NSFD over SFD for some diffusion-reaction Partial Differential Equations systems (PDEs) models, the solution of which exibits periodic oscillations and has the positivity property. In fact, NSFD schemes are also often used when you apriori know that the solution is non-negative. We also look at the possibility of extending our NSFD scheme to cases of problems that also have the advection term. Another method widely used to follow the apriori known qualitative behavior of the solution is the Exponential Fitting (EF) technique. For this reason, we also investigate the link between EF-based and NSFD-based discretization schemes for PDEs.

A nonstandard finite difference numerical method for an oscillatory diffusion-reaction problem

Conte Dajana;Pagano Giovanni
;
Paternoster Beatrice
2021

Abstract

Discretization schemes based on NonStandard Finite Differences (NSFD) are a modification of Standard Finite Differences (SFD) schemes in which the classical denominators are usually replaced by particular denominator functions that satisfy certain conditions. The main objective of such schemes is to be able to grasp some stability properties of the model analytical solution we are interested to solve, which we are not able to replicate with the classical SFD schemes. We want to investigate the advantages that come from using NSFD over SFD for some diffusion-reaction Partial Differential Equations systems (PDEs) models, the solution of which exibits periodic oscillations and has the positivity property. In fact, NSFD schemes are also often used when you apriori know that the solution is non-negative. We also look at the possibility of extending our NSFD scheme to cases of problems that also have the advection term. Another method widely used to follow the apriori known qualitative behavior of the solution is the Exponential Fitting (EF) technique. For this reason, we also investigate the link between EF-based and NSFD-based discretization schemes for PDEs.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4769543
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