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 problems with positive solutions. provides conditions obtaining solutions, which existing Euler–Maruyama method cannot do. In addition, it more accurate than non-standard finite difference (NSFD) method. Theoretically, suggested...

In this paper we develop a metastability theory for class of stochastic reaction–diffusion equations exposed to small multiplicative noise. We consider the case where unperturbed equation features multiple asymptotically stable equilibria. When system is perturbations, it likely stay near one equilibrium long period time but will eventually transition neighborhood another equilibrium. are inter...