A stochastic model for replicators in catalyzed RNA-like polymers is presented and numerically solved. The model consists of a system of reaction-diffusion equations describing the evolution of a population formed by RNA-like molecules with catalytic capabilities in a prebiotic process. The diffusion effects and the catalytic reactions are deterministic. A stochastic excitation with additive noise is introduced as a force term. To numerically solve the governing equations we apply the stochastic method of lines. A finite-difference reaction-diffusion system is constructed by discretizing the space and the associated stochastic differential system is numerically solved using a class of stochastic Runge-Kutta methods. Numerical experiments are carried out on a prototype of four catalyzed selfreplicator species along with an activated and an inactivated residues. Results are given in two space dimensions.