Numerical Methods for the 3-dimensional 2-body Problem in the Action-at-a-Distance Electrodynamics

Abstract

We develop two numerical methods to solve the differential equations with deviating arguments for the motion of two charges in the action-at-a-distance electrodynamics. Our first method uses Stürmer's extrapolation formula and assumes that a step of integration can be taken as a step of light ladder, which limits its use to shallow energies. The second method is an improvement of pre-existing iterative schemes, designed for stronger convergence and can be used at high-energies.

17 pages, 11 figures

References in corpus (1)

• On structure of solutions of 1-dimensional 2-body problem in Wheeler-Feynman electrodynamics

Cited by in corpus (3)

• Two-degree-of-freedom Hamiltonian for the time-symmetric two-body problem of the relativistic action-at-a-distance electrodynamics
• Equations of Motion for Variational Electrodynamics
• Quantization of almost-circular orbits in the Fokker action formalism. General scheme