The numerical scheme and convergence analysis of the stochastic Schnakenberg model

Résumé

This article discusses coupled nonlinear stochastic partial differential equations, specifically the
stochastic Schnakenberg model which is a reaction-diffusion system. The numerical approximation of the model
is achieved using the proposed stochastic forward Euler (SFE) scheme, which is consistent with the given system
of equations. The article also includes discussions on linear stability analysis, which shows that the proposed
SFE scheme is conditionally stable. Additionally, the convergence of the schemes is discussed in the mean square
sense. The numerical solution is obtained through simulations using the Python package for various parameter
values. The effects of randomness are also discussed. In terms of graphical behavior, the stochastic Schnakenberg
model exhibits self-replicating behavior.