This overview is devoted to splitting methods, a class of numerical integrators intended for
differential equations that can be subdivided into different problems easier to solve than the …

Splitting methods constitute a well-established class of numerical schemes for the time
integration of partial differential equations. Their main advantages over more traditional …

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 …

It is well known that Lawson methods suffer from a severe order reduction when integrating
initial boundary value problems where the solutions are not periodic in space or do not …

We derive a numerical method, based on operator splitting, to abstract parabolic semilinear
boundary coupled systems. The method decouples the linear components that describe the …

In this paper, we develop a high order finite difference boundary treatment method for the
implicit-explicit (IMEX) Runge-Kutta (RK) schemes solving hyperbolic systems with possibly …

In this article, we offer a comparison in terms of computational efficiency between two
techniques to avoid order reduction when using Strang method to integrate nonlinear initial …

In this paper a technique is suggested to avoid order reduction when using Strang method to
integrate nonlinear Schrödinger equation subject to time-dependent Dirichlet boundary …

In this paper we consider splitting methods in the presence of non-homogeneous boundary
conditions. In particular, we consider the corrections that have been described and analyzed …

In this paper, we develop the constraint energy minimizing generalized multiscale finite
element method (CEM-GMsFEM) for convection-diffusion equations with inhomogeneous …