To main content

Order theory for discrete gradient methods

Abstract

The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we derive conditions for arbitrarily high order. We derive specific results for the average vector field discrete gradient, from which we get P-series methods in the general case, and B-series methods for canonical Hamiltonian systems. Higher order schemes are presented, and their applications are demonstrated on the Hénon–Heiles system and a Lotka–Volterra system, and on both the training and integration of a pendulum system learned from data by a neural network.

Category

Academic article

Client

  • Research Council of Norway (RCN) / 231632
  • Research Council of Norway (RCN) / 309691

Language

English

Author(s)

Affiliation

  • SINTEF Digital / Mathematics and Cybernetics

Year

2022

Published in

BIT Numerical Mathematics

ISSN

0006-3835

View this publication at Cristin