Runge--Kutta methods determined from extended phase space methods for Hamiltonian systems

2023/08/12 by Robert I. McLachlan, McLachlan, Robert I · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #65P10 #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2308.06516

openalex publication_date 2023/08/12 · openalex created_date 2023/08/16 · openalex updated_date 2026/07/28

Abstract

We study two existing extended phase space integrators for Hamiltonian systems, the \em midpoint projection method and the \em symmetric projection method, showing that the first is a pseudosymplectic and pseudosymmetric Runge--Kutta method and the second is a monoimplicit symplectic Runge--Kutta method.

Cited by

• Explicit invariant-preserving integration of differential equations using homogeneous projection

Related

• Construction of symplectic (partitioned) Runge-Kutta methods with continuous stage
• Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control and more
• Quadratic projectable Runge-Kutta methods
• Two types of variational integrators and their equivalence
• Preservation of stability properties near fixed points of linear hamiltonian systems by symplectic integrators