Unrestricted Harmonic Balance A General Method to Evaluate Periodic Structures in Time and/or Space of Arbitrary Stability in Non-linear Differential Equation Systems V. Investigation of the Truncation Errors in the Case of an Exactly Solvable Non-linear System

The method of Unrestricted Harmonie Balance (UHB) is a generally applicable procedure to determine the Fourier coefficients and constants of motion (frequency, velocity) of non-linear periodic phenomena in time and space and was outlined and applied to various problems in chemistry in preceding papers. Here the truncation error is investigated by comparing the UHB results for various truncation harmonics N with the rigorous analytical solution for the Kepler problem which is one of the rare examples of an exactly solvable non-linear problem.