Looking for efficiency when avoiding order reduction in nonlinear problems with Strang splitting

TL;DR

This paper compares two techniques to prevent order reduction in nonlinear problems using Strang splitting, demonstrating the superior efficiency of Alonso et al.'s method and providing theoretical justification for one of its implementations.

Contribution

It introduces a comparative analysis of two existing techniques, showing the efficiency advantage of Alonso et al.'s approach and offering new theoretical proofs for its order.

Findings

Alonso et al.'s technique is more efficient than Einkemmer et al.'s.

One implementation of Alonso et al.'s method is theoretically justified.

The paper provides practical insights into implementing Strang splitting for nonlinear problems.

Abstract

In this paper, we offer a comparison in terms of computational efficiency between two techniques to avoid order reduction when using Strang method to integrate nonlinear initial boundary value problems with time-dependent boundary conditions. Considering different implementations for each of the techniques, we show that the technique suggested by Alonso et al. is more efficient than the one suggested by Einkemmer et al. Moreover, for one of the implementations of the technique by Alonso et al. we justify its order through the proof of some new theorems.