Title :
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
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;
Conference_Titel :
Ultrasonics Symposium (IUS), 2009 IEEE International
Conference_Location :
Rome
Print_ISBN :
978-1-4244-4389-5
Electronic_ISBN :
1948-5719
DOI :
10.1109/ULTSYM.2009.5442057
