Numerical solutions of fluctuation-induced kinetics in fractal dimensions

Fluctuation-induced kinetics of diffusion-influenced reactions in fractal dimensions have been studied. The fluctuations in concentrations of the reactants dominate the long-time dynamics and efficient numerical methods are needed to quantify the long-time fluctuation effects. We present the generalized numerical methods that are efficient especially for the investigation of the long-time dynamics. Numerical solutions of new coupled diffusion–reaction equations obtained by applying hierarchical Smoluchowski approaches to A + A → C and A + B → C reactions in fractal dimensions show that the present numerical methods produce accurate long-time results efficiently in fractal dimensions.