2011/02/10 by Tony MacKenzie, MacKenzie, Tony, A. J. Roberts +1 · 1 citation
Engineering · #Dynamics and Control of Mechanical Systems #Modular Robots and Swarm Intelligence #Slime Mold and Myxomycetes Research
paper · pdf · doi:10.48550/arxiv.1102.2037
Developments in dynamical systems theory provides new support for the discretisation of \pdes and other microscale systems. Here we explore the methodology applied to the gap-tooth scheme in the equation-free approach of Kevrekidis in two spatial dimensions. The algebraic detail is enormous so we detail computer algebra procedures to handle the enormity. However, modelling the dynamics on 2D spatial patches appears to require a mixed numerical and algebraic approach that is detailed in this report. Being based upon the computation of residuals, the procedures here may be simply adapted to a wide class of reaction-diffusion equations.