Investigating a one-dimensional Lengyel–Epstein system under the influence of multiplicative time noise

This paper investigates a one-dimensional Lengyel–Epstein (LE) system under the influence of multiplicative time noise in the Ito sense. The LE system is a dimensionless nonlinear chemical reaction–diffusion model, and it describes the oscillation in chemical reactions. Dealing with the stochastic reaction–diffusion system is a tough task. The existence of the solution is guaranteed by using the fixed-point theory. Schauder’s fixed point theorem is used to ensure that a solution exists. To gain an approximate solution of the stochastic system, finite difference techniques are applied. The approximation of the system is carried out by two different methods. The analysis of the scheme is derived in the mean square sense. Both schemes are consistent with the underlying model in the mean square sense. The von Neumann approach is used to demonstrate the linear stability of each scheme. Scheme I is von Neumann stable, while Scheme II is also stable. Scheme I displayed negative values for the concentration profiles and divergence behavior for some parameter values. The proposed scheme II showed positive solutions and converged to the steady-state point for given parameter values. The simulations illustrate the effectiveness of the time-efficient numerical techniques.