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

Author

Schiffner, Martin ; Mleczko, Michal ; Schmitz, Georg

Author_Institution

Inst. of Med. Eng., Ruhr-Univ. Bochum, Bochum, Germany

fYear

2009

fDate

20-23 Sept. 2009

Firstpage

1

Lastpage

4

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.

Keywords

Volterra series; partial differential equations; polynomials; ultrasonic propagation; Burgers equation; L2-norm; Volterra polynomial; Volterra series; boundary condition; Biomedical engineering; Biomedical imaging; Boundary conditions; Convergence of numerical methods; Kernel; Medical diagnostic imaging; Nonlinear equations; Nonlinear systems; Polynomials; Ultrasonic imaging;

fLanguage

English

Publisher

ieee

Conference_Titel

Ultrasonics Symposium (IUS), 2009 IEEE International

Conference_Location

Rome

ISSN

1948-5719

Print_ISBN

978-1-4244-4389-5

Electronic_ISBN

1948-5719

Type

conf

DOI

10.1109/ULTSYM.2009.5442057

Filename

5442057