Avoiding order reduction when integrating diffusion-reaction 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.

References in corpus (1)

• Overcoming order reduction in diffusion-reaction splitting. Part 2: oblique boundary conditions

Cited by in corpus (2)

• Order reduction and how to avoid it when Lawson methods integrate reaction-diffusion boundary value problems
• Looking for efficiency when avoiding order reduction in nonlinear problems with Strang splitting