A Reliable Computational Scheme for Stochastic Reaction–Diffusion Nonlinear Chemical Model

Abstract

The main aim of this contribution is to construct a numerical scheme for solving stochastic time-dependent partial differential equations (PDEs). This has the advantage of solving problems with positive solutions. The scheme provides conditions for obtaining positive solutions, which the existing Euler–Maruyama method cannot do. In addition, it is more accurate than the existing stochastic non-standard finite difference (NSFD) method. Theoretically, the suggested scheme is more accurate than the current NSFD method, and its stability and consistency analysis are also shown. The scheme is applied to the linear scalar stochastic time-dependent parabolic equation and the nonlinear auto-catalytic Brusselator model. The deficiency of the NSFD in terms of accuracy is also shown by providing different graphs. Many observable occurrences in the physical world can be traced back to certain chemical concentrations. Examining and understanding the inter-diffusion between chemical concentrations is important, especially when they coincide. The Brusselator model is the gold standard for describing the relationship between chemical concentrations and other variables in chemical systems. A computational code for the proposed model scheme may be made available to readers upon request for convenience.