Abstract

In this paper we study the numerical approximation of Turing patterns corresponding to steady state solutions of a PDE system of reaction-diffusion equations modeling an electrodeposition process. We apply the Method of Lines (MOL) and describe the semi-discretization by high order finite differences in space given by the Extended Central Difference Formulas (ECDFs) that approximate Neumann boundary conditions (BCs) with the same accuracy. We introduce a test equation to describe the interplay between the diffusion and the reaction time scales. We present a stability analysis of a selection of time-integrators (IMEX 2-SBDF method, Crank-Nicolson (CN), Alternating Direction Implicit (ADI) method) for the test equation as well as for the Schnakenberg model, prototype of nonlinear reaction-diffusion systems with Turing patterns. Eventually, we apply the ADI-ECDF schemes to solve the electrodeposition model until the stationary patterns (spots & worms and only spots) are reached. We validate the model by comparison with experiments on Cu film growth by electrodeposition.

Autore Pugliese

• Sgura Ivonne , Bozzini Benedetto

Tutti gli autori

• I. Sgura , B. Bozzini , D. Lacitignola

Titolo volume/Rivista

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Anno di pubblicazione

2012

ISSN

0377-0427

ISBN

Non Disponibile

Numero di citazioni Wos

17

Ultimo Aggiornamento Citazioni

28/04/2018

Numero di citazioni Scopus

18

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile