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)=(Au(⋅,t))(x)+f(x,u(x,t)), where AA 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.