Automatic code generator for higher order integrators

Published: 1 May 2014| Version 1 | DOI: 10.17632/t37wbm7c2j.1
Asif Mushtaq, Kåre Olaussen


Abstract Some explicit algorithms for higher order symplectic integration of a large class of Hamilton’s equations have recently been discussed by Mushtaq et al. Here we present a Python program for automatic numerical implementation of these algorithms for a given Hamiltonian, both for double precision and multiprecision computations. We provide examples of how to use this program, and illustrate behavior of both the code generator and the generated solver module(s). Title of program: HOMsPy Catalogue Id: AESD_v1_0 Nature of problem We have developed algorithms [5] for numerical solution of Hamilton's equations. qdot a = ΔH(q,p)/Δp a , pdot a = -ΔH(q,p)/Δq a , a=1.....,N (1) for Hamiltonians of the form H(q,p)= T(p) + V(q) = 1/2p T M p +V(q), (2) with M a symmetric positive definite matrix. The algorithms preserve the symplectic property of the time evolution exactly, and are of orders Τ N (for 2 ≤N ≤ 8) in the timestep Τ. Although explicit, the algorithms are time-consuming and error-prone to implement numerically by hand, ... Versions of this program held in the CPC repository in Mendeley Data AESD_v1_0; HOMsPy; 10.1016/j.cpc.2014.01.012 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)



Computational Physics, Computer Algebra System, Computational Method