Analysis of error propagation in the RK3GL2 method

TL;DR

This paper analytically examines how local errors propagate in the RK3GL2 numerical method, revealing that it maintains a global order of four despite its hybrid design.

Contribution

It provides an analytical study of error propagation in RK3GL2, demonstrating its expected global order of four, which was previously unconfirmed.

Findings

Global order of RK3GL2 is four.

Error propagation analysis confirms theoretical order.

Hybrid method maintains high accuracy.

Abstract

The RK3GL2 method is a numerical method for solving initial value problems in ordinary differential equations, and is a hybrid of a third-order Runge-Kutta method and two-point Gauss-Legendre quadrature. In this paper we present an analytical study of the propagation of local errors in this method, and show that the global order of RK3GL2 is expected to be four.