Eight-stage pseudo-symplectic Runge-Kutta methods of order (4, 8)

TL;DR

This paper introduces a family of 8-stage pseudo-symplectic Runge-Kutta methods of order (4, 8), designed to preserve symplectic structure up to high order, with an example of a 7-stage method of order (4, 9).

Contribution

It derives a new family of pseudo-symplectic Runge-Kutta methods using symmetry assumptions, extending the order and structure preservation capabilities.

Findings

Developed 8-stage methods of order (4, 8)

Provided a 7-stage example of order (4, 9)

Enhanced symplectic structure preservation in numerical methods

Abstract

Using simplifying assumptions that are related to the time reversal symmetry, a 1-dimensional family of 8-stage pseudo-symplectic Runge-Kutta methods of order (4, 8), i.e., methods of order 4 that preserve symplectic structure up to order 8, is derived. An example of 7-stage method of order (4, 9) is given.