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

摘要

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.