Trotter products and reaction–diffusion equations

In this paper, we study a class of generalized diffusion–reaction equations of the form ∂ u ∂ t ( x , t ) = ( A u ( ⋅ , t ) ) ( x ) + f ( x , u ( x , t ) ) , where A is a pseudodifferential operator which generates a Feller semigroup. Using the Trotter product formula we give a corresponding discrete time integro-difference equation for numerical solutions.