Avoiding order reduction when integrating reaction–diffusion boundary value problems with exponential splitting methods

Abstract

In this paper, we suggest a technique to avoid order reduction in time when integrating reaction–diffusion boundary value problems under non-homogeneous boundary conditions with exponential splitting methods. More precisely, we consider Lie–Trotter and Strang splitting methods and Dirichlet, Neumann and Robin boundary conditions. Beginning from an abstract framework in Banach spaces, a thorough error analysis after full discretization is performed and some numerical results are shown which corroborate the theoretical results.