Evaluation of an analytical solution to the Burgers equation based on Volterra series

Martin Schiffner, Michal Mleczko, Georg Schmitz

Proc IEEE International Ultrasonics Symposium, 2009, pp. 385 - 388, DOI: 10.1109/ULTSYM.2009.5442057


Abstract

A simple, well-interpretable, and explicit analytical solution to the Burgers equation based on Volterra series is derived. Its region of convergence is investigated and a method for the computationally efficient numerical evaluation of the associated Volterra polynomials is presented. For a given boundary condition, numerical results are compared to a widely-used numerical standard solution. After a propagation distance of 10 cm in steps of 5 mm the Volterra polynomials of degree 2 and 3 achieve relative errors in terms of the L2-norm of 4.22% and 1.35%, respectively.

[DOI] [accepted paper] [bibtex]

Tags: Burgers equation, nonlinear acoustics, nonlinear sound propagation, nonlinear system theory, Volterra