On the Construction of Splitting Methods by Stabilizing Corrections with Runge-Kutta Pairs

TL;DR

This paper presents a general procedure for constructing splitting methods using Runge-Kutta pairs, analyzing their stability, and demonstrating their effectiveness through numerical tests.

Contribution

It introduces a novel method to build internally consistent splitting schemes from explicit and diagonally implicit Runge-Kutta pairs, including stability analysis and numerical validation.

Findings

Stable splitting methods with Runge-Kutta pairs are constructed.

Numerical tests confirm the effectiveness of the proposed methods.

Linear stability properties are thoroughly analyzed.

Abstract

In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta methods. The procedure will be applied to suitable second-order pairs, and we will consider methods with or without a mass conserving finishing stage. For these splitting methods, the linear stability properties are studied and numerical test results are presented.