Spatio-temporal organization in a reaction-diffusion model for alloy electrodeposition. Part II: numerical issues

Ivonne Sgura

Dip. Matematica e Fisica "Ennio De Giorgi", Univ. Salento, Lecce, Italy

This presentation focus on the numerical issues related to the
mathematical modeling work highlighted in the previous talk by D.
Lacitignola. Numerical approximation of Turing patterns and spiral
waves is a challenging task:

i) high accuracy in space and longtime integration are needed to obtain stationary patterns;

ii) structures oscillating in space and time are expected for
solutions in the Hopf region. We perform space semi-discretization
by Extended Central Difference Formulas of order p=2,4,6
(ECDF_p). For time discretization, we introduce a test equation
and define its stability region in terms of reaction and diffusion
time scales. We present a stability analysis for a selection of
time-integrators (IMEX and Symplectic Euler, 2-SBDF, ADI schemes)
and compare them in terms of stepsize restriction by solving the
Schnackenberg system, prototype of reaction-diffusion system with
Turing patterns. Eventually, we apply the ADI-ECDF_p to the
electrodeposition model in order to approximate both stationary and oscillating Turing patterns and spiral waves. We validate the
morphochemical model by comparing numerical solutions with experimental data.


Work in collaboration with Benedetto Bozzini (Dip. Ingegneria dell'Innovazione, Univ del Salento, Lecce)