Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
On the stability of implicit-explicit linear multistep methods
Applied Numerical Mathematics - Special issue on time integration
Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations
Recent trends in numerical analysis
An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
IRKC: an IMEX solver for stiff diffusion-reaction PDEs
Journal of Computational and Applied Mathematics
Velocity-induced numerical solutions of reaction-diffusion systems on continuously growing domains
Journal of Computational Physics
IMEX Runge-Kutta schemes for reaction-diffusion equations
Journal of Computational and Applied Mathematics
High-order finite difference schemes for the solution of second-order BVPs
Journal of Computational and Applied Mathematics
An efficient and robust numerical algorithm for estimating parameters in Turing systems
Journal of Computational Physics
Travelling waves in a reaction-diffusion model for electrodeposition
Mathematics and Computers in Simulation
Hi-index | 7.29 |
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.