Table of Contents
International Journal of Computational Mathematics
Volume 2015 (2015), Article ID 212860, 13 pages
http://dx.doi.org/10.1155/2015/212860
Research Article

Numerical Solvability and Solution of an Inverse Problem Related to the Gibbs Phenomenon

Center for Research in Applied Mathematics & Statistics (CRAMS), AUL, P.O. Box 14-6495, Cola, Beirut, Lebanon

Received 7 March 2015; Accepted 10 May 2015

Academic Editor: Don Hong

Copyright © 2015 Nassar H. S. Haidar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We report on the inverse problem for the truncated Fourier series representation of in a form with a quadratic degeneracy, revealing the existence of the Gibbs-Wilbraham phenomenon. A new distribution-theoretic proof is proposed for this phenomenon. The paper studies moreover the iterative numerical solvability and solution of this inverse problem near discontinuities of .