Next Article in Journal
Emergence of an Aperiodic Dirichlet Space from the Tetrahedral Units of an Icosahedral Internal Space
Previous Article in Journal
Analysis of Magneto-hydrodynamics Flow and Heat Transfer of a Viscoelastic Fluid through Porous Medium in Wire Coating Analysis
Article Menu

Export Article

Open AccessArticle
Mathematics 2017, 5(2), 28; doi:10.3390/math5020028

A Two-Stage Method for Piecewise-Constant Solution for Fredholm Integral Equations of the First Kind

Department of Mathematics, Shantou University, Shantou 515063, China
*
Author to whom correspondence should be addressed.
Academic Editor: Lokenath Debnath
Received: 18 December 2016 / Revised: 12 May 2017 / Accepted: 16 May 2017 / Published: 22 May 2017
View Full-Text   |   Download PDF [999 KB, uploaded 22 May 2017]   |  

Abstract

A numerical method is proposed for estimating piecewise-constant solutions for Fredholm integral equations of the first kind. Two functionals, namely the weighted total variation (WTV) functional and the simplified Modica-Mortola (MM) functional, are introduced. The solution procedure consists of two stages. In the first stage, the WTV functional is minimized to obtain an approximate solution f TV * . In the second stage, the simplified MM functional is minimized to obtain the final result by using the damped Newton (DN) method with f TV * as the initial guess. The numerical implementation is given in detail, and numerical results of two examples are presented to illustrate the efficiency of the proposed approach. View Full-Text
Keywords: Fredholm integral equation of the first kind; regularization; piecewise-constant solution; total variation (TV) functional; Modica-Mortola (MM) functional Fredholm integral equation of the first kind; regularization; piecewise-constant solution; total variation (TV) functional; Modica-Mortola (MM) functional
Figures

Figure 1

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. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Lin, F.-R.; Yang, S.-W. A Two-Stage Method for Piecewise-Constant Solution for Fredholm Integral Equations of the First Kind. Mathematics 2017, 5, 28.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top