Error analysis of splitting methods for inhomogeneous evolution equations

In this paper we study the convergence properties of splitting methods for inhomogeneous evolution equations. We work in an abstract Banach space setting of maximal dissipative operators. This framework allows us to study certain parabolic equations and their spatial discretizations. Under natural assumptions on the data, the Lie splitting and the trapezoidal splitting turn out to be first- and second-order convergent, respectively. An example of a parabolic equation illustrating the theoretical assumptions is given. Numerical results are included.